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lDLqrsye-rQ | that if there's no driver there your ride request will be blocked and it'll be dropped no but what I mean is might decision as to whether or not to even make the request that my available drag yeah yeah so so that's a really good point so first of all when I said earlier that I wasn't dealing with ETA that's what I meant that I'm not modeling so in queueing models where you think | 1,021 | 1,041 | https://www.youtube.com/watch?v=lDLqrsye-rQ&t=1021s | Dynamic Pricing in Ride-Sharing Platforms | |
lDLqrsye-rQ | about and you know this is not necessarily something specific to me I'd say that this type of trade-off exists everywhere let's just think about like so I'm using a model where essentially the passengers cost is blocking right they may not get served well in a real queuing system like blocking and delay are not completely dissimilar from each other in the sense that if I get blocked but that | 1,041 | 1,060 | https://www.youtube.com/watch?v=lDLqrsye-rQ&t=1041s | Dynamic Pricing in Ride-Sharing Platforms | |
lDLqrsye-rQ | really is saying is I just have to wait longer to get done with whatever I want to get done right and so I I think like the right there's two ways you can think about blocking it's like actually what the cost is it's I tried to get a ride and I couldn't say New Year's Eve or you could think about it as I didn't get the right and that means I have to wait you know longer to | 1,060 | 1,076 | https://www.youtube.com/watch?v=lDLqrsye-rQ&t=1060s | Dynamic Pricing in Ride-Sharing Platforms | |
lDLqrsye-rQ | be able to get a ride and and I think I think if this is a very very course sort of 0th order approximation to the right thing to do and the right thing to do would be to actually include ETS in the model and model that yeah that's a good question okay so that's the drivers so let me just quickly run through what the queueing model is basically the queueing model is now when I be my queueing model | 1,076 | 1,099 | https://www.youtube.com/watch?v=lDLqrsye-rQ&t=1076s | Dynamic Pricing in Ride-Sharing Platforms | |
lDLqrsye-rQ | isn't in describing this to you I'm not going to say anything about why drivers and passengers are coming in at the rates that they're coming in they just are and then let's so I've already told you that I have some model that's strategic for how I'll determine the rate at which rides are requested how I'll determine the rate at which drivers actually entered the system now let me | 1,099 | 1,115 | https://www.youtube.com/watch?v=lDLqrsye-rQ&t=1099s | Dynamic Pricing in Ride-Sharing Platforms | |
lDLqrsye-rQ | tell you sort of what actually happens inside the model but those you know rates of arrival of drivers and passengers so basically drivers enter at some rate lambda and when there's a drivers available ride requests arrive at some rate which depends on the number of available drivers that's what we computed earlier um if a driver is available the ride is served otherwise | 1,115 | 1,133 | https://www.youtube.com/watch?v=lDLqrsye-rQ&t=1115s | Dynamic Pricing in Ride-Sharing Platforms | |
lDLqrsye-rQ | it's blocked rides lasts an exponential time with mean tau in the network model this sort of involves a random walk around the network so it's a little more complicated than that and after right completions this is another point where I think someone could do something interesting with this so after ride completion there's some exogenous probability that the driver signs out or | 1,133 | 1,152 | https://www.youtube.com/watch?v=lDLqrsye-rQ&t=1133s | Dynamic Pricing in Ride-Sharing Platforms | |
lDLqrsye-rQ | it becomes available okay so another thing that could be interesting that you can do here is make the exit probability dependent on their experience in the system for obvious reasons that leads to a much more complicated game so this is a you know far simplified version of that I would say that I'm actually less sort of concerned about this assumption that this is exogenous because drivers | 1,152 | 1,170 | https://www.youtube.com/watch?v=lDLqrsye-rQ&t=1152s | Dynamic Pricing in Ride-Sharing Platforms | |
lDLqrsye-rQ | are still making entry decisions based on their kind of expected earnings in the platform so it's not as if they're completely ignoring how they're going to do but I think if you wanted to refine it a bit you could think about making this something which is endogenous okay so that's that's basically the the model of what's going on and so if you look at the picture of what's happening here | 1,170 | 1,185 | https://www.youtube.com/watch?v=lDLqrsye-rQ&t=1170s | Dynamic Pricing in Ride-Sharing Platforms | |
lDLqrsye-rQ | there's two reasons that there's available drivers there's either new entry from the outside world or there's a driver who was busy who became available and and came back into the system who chose not to exit okay so there's some queue that's going up and down available drivers coming in and then when rides are requested this cue gets served down okay so a major sort of simplification for us | 1,185 | 1,206 | https://www.youtube.com/watch?v=lDLqrsye-rQ&t=1185s | Dynamic Pricing in Ride-Sharing Platforms | |
lDLqrsye-rQ | and one of the reasons for exactly the lining of the assumptions we had is that this type of queueing model turns out to be what's called a Jackson Network and this is more generally true for the network model and Jackson networks are great because they're steady-state distribution is a product alright so despite the fact that there's all these dependencies in the queuing | 1,206 | 1,221 | https://www.youtube.com/watch?v=lDLqrsye-rQ&t=1206s | Dynamic Pricing in Ride-Sharing Platforms | |
lDLqrsye-rQ | network the the steady-state distribution has the property that in steady state the queue lengths in the different you know parts of the network look like they're independent okay so in particular here what it means is that the number of available drivers is something which we have like an exact expression for the for the for the steady-state distribution okay so I'll | 1,221 | 1,241 | https://www.youtube.com/watch?v=lDLqrsye-rQ&t=1221s | Dynamic Pricing in Ride-Sharing Platforms | |
lDLqrsye-rQ | skip this slide I sorry I won't go through everything in detail what I mean is I just want to tell you what an equilibrium of our system is so an equilibrium of our system involves basically saying I connect together the strategic behavior of the passengers and drivers the pricing policy and the queueing model and so what I do is I say okay let me take the queueing model | 1,241 | 1,259 | https://www.youtube.com/watch?v=lDLqrsye-rQ&t=1241s | Dynamic Pricing in Ride-Sharing Platforms | |
lDLqrsye-rQ | compute a steady-state distribution from it using the steady-state distribution for every driver I can work out what is their expected earnings that they'll make while they're in the system and what's the expected time they're gonna live I can use that to then work out what's the entry rate of drivers and then for every passenger I can work out you know sort of for the passenger kind | 1,259 | 1,278 | https://www.youtube.com/watch?v=lDLqrsye-rQ&t=1259s | Dynamic Pricing in Ride-Sharing Platforms | |
lDLqrsye-rQ | of the steady-state condition is easy it's the same one we had before that passengers will enter as long as the price is going to be is going to be lower than their reservation value and that goes in the entry rate of ride requests so all this comes back together again and I need a consistency check that the steady-state distribution actually came from these things that I | 1,278 | 1,294 | https://www.youtube.com/watch?v=lDLqrsye-rQ&t=1278s | Dynamic Pricing in Ride-Sharing Platforms | |
lDLqrsye-rQ | just computed alright so you can do that and that's kind of a definition of a system equilibrium in our model and you know what we show is that basically as long as you have very mild regularity conditions on the system namely among other things that the price increases when the number of available drivers decreases so this is a condition on the pricing function then equilibria always | 1,294 | 1,313 | https://www.youtube.com/watch?v=lDLqrsye-rQ&t=1294s | Dynamic Pricing in Ride-Sharing Platforms | |
lDLqrsye-rQ | exist and their unique under reasonable sort of smoothness conditions so oh we go that that is so let me talk about sort of nicely smooth those conditions here I mean on the distributions so let me let me sort of move on to how we want to use this so I guess you know part half the talk is like here's a model that sort of sits on some knife at knife edge of tractability and still capturing a bunch | 1,313 | 1,336 | https://www.youtube.com/watch?v=lDLqrsye-rQ&t=1313s | Dynamic Pricing in Ride-Sharing Platforms | |
lDLqrsye-rQ | of effects that are important I've already pointed out to you at least five or six different ways that I think you would want to do things to the model to capture effects that are that are important in practice that said at least in our experience thinking about it adding any one of those things made the model much harder to work with so in order to in order to make progress | 1,336 | 1,353 | https://www.youtube.com/watch?v=lDLqrsye-rQ&t=1336s | Dynamic Pricing in Ride-Sharing Platforms | |
lDLqrsye-rQ | beyond what we had I think part of the question is going to be you know where you get technical simplicity despite having at it in these communities additional complications and I think one thing for us even with the model that we had that is very helpful is to use awesome products to simplify the analysis this is something which is now by now very standard in in analyzing | 1,353 | 1,369 | https://www.youtube.com/watch?v=lDLqrsye-rQ&t=1353s | Dynamic Pricing in Ride-Sharing Platforms | |
lDLqrsye-rQ | these types of matching markets Eric bhootish and Eduardo Acevedo have a really nice paper that sort of talks about some of the things that you can do using this type of approach so in our case the the limiting approach that we use is that we have a sequence of systems we consider in the end system I'm basically scaling up the exogenous rates the arrival rates of passengers | 1,369 | 1,389 | https://www.youtube.com/watch?v=lDLqrsye-rQ&t=1369s | Dynamic Pricing in Ride-Sharing Platforms | |
lDLqrsye-rQ | and of drivers and in the end system I have some pricing policy that's actually indexed by in okay and I'll talk to you a little bit about how that how that works so in each system this gives rise to a system equilibrium and we basically analyze pricing by looking at the asymptotics of these equilibrium ok so that's what I'm going to show you I'll show you a bunch of pictures that | 1,389 | 1,405 | https://www.youtube.com/watch?v=lDLqrsye-rQ&t=1389s | Dynamic Pricing in Ride-Sharing Platforms | |
lDLqrsye-rQ | explain what's going on and there's corresponding theorems behind it so let me start with static pricing again static pricing doesn't mean there's a single multiplier the whole day it means that I have a predictable uncertainty on the order of hours or something like that that I use to set a multiplier but I don't change the multiplier on the basis of the exact number of available | 1,405 | 1,426 | https://www.youtube.com/watch?v=lDLqrsye-rQ&t=1405s | Dynamic Pricing in Ride-Sharing Platforms | |
lDLqrsye-rQ | drivers that are in the system so but you should be thinking when I say static is that idiosyncratic stochastic fluctuations are not being captured by the by the dynamic pricing policy so so in math this means that P of a is a constant for all a that no matter what the level of the queue is I'm setting the same multiplier so there's a theorem here that you know don't worry about | 1,426 | 1,447 | https://www.youtube.com/watch?v=lDLqrsye-rQ&t=1426s | Dynamic Pricing in Ride-Sharing Platforms | |
lDLqrsye-rQ | reading the technical sort of expressions carefully but here's basically what's going on what it says is that you pick the multiplier that you're going to use at all eh okay once you've done that then if I scale and there's there's this should be scaled by and this should be our n over and its a scaled completed it's obviously the rate of completed rides is going to go to infinity if if n | 1,447 | 1,468 | https://www.youtube.com/watch?v=lDLqrsye-rQ&t=1447s | Dynamic Pricing in Ride-Sharing Platforms | |
lDLqrsye-rQ | goes to infinity it's the scaled rate of completed rides that that's normalized so if I take our n over n the rate of completed rides divided by n that has a really natural sort of interpretation imagine sort of two unconstrained systems one in which as a passenger whenever I request a ride there's always a driver waiting for me all right and another in which as a driver whenever I | 1,468 | 1,489 | https://www.youtube.com/watch?v=lDLqrsye-rQ&t=1468s | Dynamic Pricing in Ride-Sharing Platforms | |
lDLqrsye-rQ | finish driving there's always a passenger right there requesting a ride that I can get matched to okay so in one of them demand is not a canoe in the first system I just described supply is not a constraint the second one demand is not a constraint so each of these two sort of naturally give you a supply curve in a demand curve this expression is basically how many drivers would | 1,489 | 1,508 | https://www.youtube.com/watch?v=lDLqrsye-rQ&t=1489s | Dynamic Pricing in Ride-Sharing Platforms | |
lDLqrsye-rQ | enter if they knew that whenever they were available there would be a passenger immediately there for them and this expression is how many passengers would enter if they knew that whenever they requested a ride there would be immediately be a driver there to serve them that's the same entry rate we had before and so that's that's what put is basically available the throughput is a | 1,508 | 1,525 | https://www.youtube.com/watch?v=lDLqrsye-rQ&t=1508s | Dynamic Pricing in Ride-Sharing Platforms | |
lDLqrsye-rQ | min of available supply and available demand so that's really nice because you can visualize it as sort of a demand and supply curve crossing each other this green curve here is the demand curve this green curve here is the supply curve they cross right at this point now what's the x-axis this is different than a usual plot in in economics the x-axis here is price the y-axis is throughput | 1,525 | 1,545 | https://www.youtube.com/watch?v=lDLqrsye-rQ&t=1525s | Dynamic Pricing in Ride-Sharing Platforms | |
lDLqrsye-rQ | so I'll tell you about the red curves in a second so what I'm saying here is that you pick a multiplier on the x-axis and the the actual throughput that you're going to see in the system is the minimum of this green curve and this green curve okay so this sort of pyramid shape thing is what the overall throughput is as you vary the multiplier and you can see that if your only choice | 1,545 | 1,565 | https://www.youtube.com/watch?v=lDLqrsye-rQ&t=1545s | Dynamic Pricing in Ride-Sharing Platforms | |
lDLqrsye-rQ | was what multiplier to pick and you didn't have any dynamic pricing available the multiplier you would pick is the one where they intersect right that's the peak and so that's that's what we're gonna call that the balance price for the rest of the talk the red curves are just depicting what happens as n increases all right so these are simulations for finite n and the green | 1,565 | 1,581 | https://www.youtube.com/watch?v=lDLqrsye-rQ&t=1565s | Dynamic Pricing in Ride-Sharing Platforms | |
lDLqrsye-rQ | is the theory in the in the limiting system all right everybody okay with that so basically what I'm saying is that there's like a natural notion of available supply and available demand and I can use that to say that if what I want to do is maximize throughput then the multiplier would pick is the one balances the two of them it's pretty intuitive it's just nice to get that out | 1,581 | 1,601 | https://www.youtube.com/watch?v=lDLqrsye-rQ&t=1581s | Dynamic Pricing in Ride-Sharing Platforms | |
lDLqrsye-rQ | of the out of out of the primitives so I'll skip this slide I just said that so now let's talk about dynamic pricing and what we did is we decided to focus on a particular family of dynamic pricing policies there's there's a small part of the paper that says something on slightly more complex policies but it's actually it is actually a little bit harder to deal with sort of arbitrary | 1,601 | 1,621 | https://www.youtube.com/watch?v=lDLqrsye-rQ&t=1601s | Dynamic Pricing in Ride-Sharing Platforms | |
lDLqrsye-rQ | dynamic pricing policies and come up with exactly the same conclusions so what we do is we focus on threshold policies and and these are very natural because they match exactly with what's done in practice which is basically that I have a threshold and then if the number of available drivers drops below that threshold I set a multiplier that's a high multiplier if the number of driver | 1,621 | 1,644 | https://www.youtube.com/watch?v=lDLqrsye-rQ&t=1621s | Dynamic Pricing in Ride-Sharing Platforms | |
lDLqrsye-rQ | available drivers goes above that threshold I set a multiplier that's a low multiplier okay so I'm kind of moving between these two multipliers the slightly more general thing we looked at is a finite number of thresholds okay and then you know the more general thing obviously would be that the the price curve can be anything across the number of Avila's and so this has kind of | 1,644 | 1,661 | https://www.youtube.com/watch?v=lDLqrsye-rQ&t=1644s | Dynamic Pricing in Ride-Sharing Platforms | |
lDLqrsye-rQ | inspired the reason we specifically focused on this is because we wanted to try to say something about what search and prime-time policies are actually doing and they basically have this flavor that there's kind of thresholds that when they're crossed the the multiplier is going to go up or down as a result okay so I think I can convey kind of what our theorem is with | 1,661 | 1,680 | https://www.youtube.com/watch?v=lDLqrsye-rQ&t=1661s | Dynamic Pricing in Ride-Sharing Platforms | |
lDLqrsye-rQ | pictures more easily than the results I'll show you in a second so let's let me just sort of parse this picture for you okay so on the x-axis sorry on the x-axis what I'm plotting again is the multiplier right so it's going from from 0 up to 5 here that's the price multiplier that I'm going to use the blue curve is the throughput that I obtain if I just set that multiplier | 1,680 | 1,705 | https://www.youtube.com/watch?v=lDLqrsye-rQ&t=1680s | Dynamic Pricing in Ride-Sharing Platforms | |
lDLqrsye-rQ | regardless of the number of available drivers same basically as the curves that were showing you in the previous graph which is pure static pricing okay the purple curve is what I get with a very particular dynamic pricing policy the dynamic pricing policy is one where one of the two multipliers is set at green at this at this point right here and the other multiplier is the one | 1,705 | 1,725 | https://www.youtube.com/watch?v=lDLqrsye-rQ&t=1705s | Dynamic Pricing in Ride-Sharing Platforms | |
lDLqrsye-rQ | that's bearing on the x-axis okay now what does that mean if I'm on this side then it means is that the high multiplier is this value and the low multiplier is down here and if I'm on this side it means that the low multiplier is this value and high multiplier is the one on this axis that make sense okay so that's that's kind of how you can do a 1d visualization of a family of dynamic | 1,725 | 1,747 | https://www.youtube.com/watch?v=lDLqrsye-rQ&t=1725s | Dynamic Pricing in Ride-Sharing Platforms | |
lDLqrsye-rQ | pricing policies in this graph and that's also why there's a kink right here okay so this then the purple curve is the throughput that I get with that particular dynamic pricing policy as I vary on the x-axis and what I'll do is I'll just make n larger and as n gets larger what you notice is what you should see is that the static curve and the dynamic curve the peaks are going to | 1,747 | 1,768 | https://www.youtube.com/watch?v=lDLqrsye-rQ&t=1747s | Dynamic Pricing in Ride-Sharing Platforms | |
lDLqrsye-rQ | come together okay and so that's what happens in the limit here so this this is the limiting value with n going to infinity the purple curve is what I get from dynamic pricing again defined the way that I talked about it where this is one of the two prices and the other price is varying on the x-axis and the blue curve is the one I just showed you a few minutes ago which is what I get | 1,768 | 1,788 | https://www.youtube.com/watch?v=lDLqrsye-rQ&t=1768s | Dynamic Pricing in Ride-Sharing Platforms | |
lDLqrsye-rQ | from static pricing and what's the important point to notice from this graph is that both of them coincide at their peak okay so what that's basically saying is that in the fluid limit and this in this kind of hydrodynamic limit where we're scaling you know down by n that you're not getting anything by using a dynamic pricing policy over a static pricing policy you know there's a | 1,788 | 1,807 | https://www.youtube.com/watch?v=lDLqrsye-rQ&t=1788s | Dynamic Pricing in Ride-Sharing Platforms | |
lDLqrsye-rQ | bunch of suppressed in these graphs okay number one it's numeric so obviously I haven't convinced you about other potential values for prices that I could use number two I didn't say anything about the threshold right so like what's going on with the threshold and so in I'll show you the theorem in a second one of one of the things we're doing in the background here is that as n is | 1,807 | 1,823 | https://www.youtube.com/watch?v=lDLqrsye-rQ&t=1807s | Dynamic Pricing in Ride-Sharing Platforms | |
lDLqrsye-rQ | getting larger we're varying the threshold that we use and we're doing so in an optimal way given the two prices that are chosen right so we're kind of favorably biasing the dynamic pricing policy to pick the best threshold that we could given the two prices that were used and so really the result is saying here is feel free to pick the threshold and the two prices however you want and | 1,823 | 1,841 | https://www.youtube.com/watch?v=lDLqrsye-rQ&t=1823s | Dynamic Pricing in Ride-Sharing Platforms | |
lDLqrsye-rQ | you're never gonna do better than what what static pricing gets you yeah okay now B I should be done before that already okay so this is the limit and what it basically says is let our n star be the rate of completed rides in the n system using the optimal static price and let our n double star be the rate of completed rise in the n system using the optimal threshold pricing strategy | 1,841 | 1,865 | https://www.youtube.com/watch?v=lDLqrsye-rQ&t=1841s | Dynamic Pricing in Ride-Sharing Platforms | |
lDLqrsye-rQ | then if the valuation distribution has a monotone hazard rate I'll talk more about this in a second then the the difference between these two scaled by n goes to zero okay so some comments on this first of all I want to point out so there's this is a really important restriction in the result and the proof of the result what ends up happening is that we need to look at sort of how the | 1,865 | 1,890 | https://www.youtube.com/watch?v=lDLqrsye-rQ&t=1865s | Dynamic Pricing in Ride-Sharing Platforms | |
lDLqrsye-rQ | level of demand changes as you vary the pricing policy and it turns out that some condition on the valuation distribution is is sort of necessary it's a little bit looser than this it doesn't quite have to be that strong that that's probably most interpretable definition what's interesting is that there's no condition on the on the Preferences of the drivers FC does not | 1,890 | 1,908 | https://www.youtube.com/watch?v=lDLqrsye-rQ&t=1890s | Dynamic Pricing in Ride-Sharing Platforms | |
lDLqrsye-rQ | enter into this theorem so FC could be arbitrary it's the the restriction is only on that fee okay that's one point the second point is I guess what I find interesting about this result it the way I would state it I I think like the the more glib statement is there's no value to dynamic pricing I think the way I would stated that's a bit more precise is that there's only second-order | 1,908 | 1,927 | https://www.youtube.com/watch?v=lDLqrsye-rQ&t=1908s | Dynamic Pricing in Ride-Sharing Platforms | |
lDLqrsye-rQ | benefit to dynamic pricing right so to the extent that you see benefits from dynamic pricing it's happening because it's happening because you're actually able to sort of correct things in the in the sort of a Gaussian term not in the not in the fluid term the third comment I want to make is that maybe one naive view you might have on this result as well of course because you took the | 1,927 | 1,945 | https://www.youtube.com/watch?v=lDLqrsye-rQ&t=1927s | Dynamic Pricing in Ride-Sharing Platforms | |
lDLqrsye-rQ | limit you got rid of all stochasticity but the thing is that's not true so that the drivers went there is actually a well-defined steady state distribution that's seen sorry/not drivers by passengers when they enter even in the limiting system okay so when a passenger arrives it is the case that the the number of available drivers that they see is a random variable and that | 1,945 | 1,964 | https://www.youtube.com/watch?v=lDLqrsye-rQ&t=1945s | Dynamic Pricing in Ride-Sharing Platforms | |
lDLqrsye-rQ | remains true even when you pass to the limit okay so it's it is true that we're speeding up the system but from a passengers perspective they're always reacting an instantaneous state so that stochasticity is still relevant and then i think that's part of what makes the makes the fact that this happens a little bit surprising so one comment i want to make is that | 1,964 | 1,982 | https://www.youtube.com/watch?v=lDLqrsye-rQ&t=1964s | Dynamic Pricing in Ride-Sharing Platforms | |
lDLqrsye-rQ | these types of results are similar to stuff that's kind of long-standing in the revenue management literature where in the early results in that literature you know it was established that that fluid pricing policies of the sort that we were talking about are not going to be better than dynamic pricing and there's been a lot of work extending those types of results but one | 1,982 | 2,000 | https://www.youtube.com/watch?v=lDLqrsye-rQ&t=1982s | Dynamic Pricing in Ride-Sharing Platforms | |
lDLqrsye-rQ | interesting thing in that literature is they're not really been any work that looks at two-sided markets so that literature usually what happens is you're kind of given a fixed basket of stuff to sell and then you're allowed to use whatever mechanism you want to sell up to a deadline and like the canonical example is airline tickets so you're an airline you're selling seats and so you | 2,000 | 2,016 | https://www.youtube.com/watch?v=lDLqrsye-rQ&t=2000s | Dynamic Pricing in Ride-Sharing Platforms | |
lDLqrsye-rQ | have like planes that are empty and you have a bunch of seats to sell up to a deadline when the plane actually takes off you're allowed to use whatever pricing policy you want to set prices for the seats okay in our case kind of one of the things I think that makes this really interesting is that we have this you know that the seats are strategic the seats are the drivers and | 2,016 | 2,033 | https://www.youtube.com/watch?v=lDLqrsye-rQ&t=2016s | Dynamic Pricing in Ride-Sharing Platforms | |
lDLqrsye-rQ | and they're they're entering because of because of what we're doing so you know that's one of the big differences and so again just to point out kind of why this is interesting to work on is I think there are if you look at the problems that are faced by many platforms in managing inventory internally so the analog in air B&B would be sort of managing the inventory of hotel rooms | 2,033 | 2,051 | https://www.youtube.com/watch?v=lDLqrsye-rQ&t=2033s | Dynamic Pricing in Ride-Sharing Platforms | |
lDLqrsye-rQ | they look like classic revenue management problems but with strategic supply and so that that you know that perspective is something which opens up I think a range of algorithmic insight that isn't there yet in the literature so I'm going to skip the proof just because we're already well over time for this session I'm happy to talk to you about that offline if you want or if you | 2,051 | 2,072 | https://www.youtube.com/watch?v=lDLqrsye-rQ&t=2051s | Dynamic Pricing in Ride-Sharing Platforms | |
lDLqrsye-rQ | play back the video and look at the slide slowly you should be able to make it out so last thing I'll tell you is and this result I think is less surprising it's just I just like it because of the nature of how we formulated it so dynamic pricing is obviously helpful all right and and already there's a hint in this second-order effect that I mentioned and really like why do we use it well one | 2,072 | 2,091 | https://www.youtube.com/watch?v=lDLqrsye-rQ&t=2072s | Dynamic Pricing in Ride-Sharing Platforms | |
lDLqrsye-rQ | reason we use it is because we don't want to have to sit and futz around with what we think the system parameters are actually going to be even when it's predictable uncertainty all right so one thing that's nice about dynamic pricing is it sort of naturally adjusts itself to wherever the system is living okay and somehow you would like to be able to make a statement that that captures that | 2,091 | 2,108 | https://www.youtube.com/watch?v=lDLqrsye-rQ&t=2091s | Dynamic Pricing in Ride-Sharing Platforms | |
lDLqrsye-rQ | robustness that if the system parameters are known yeah then maybe static pricing is at least as good as there never is you know doing as good as dynamic pricing but when system parameters are unknown presumably you should gain something in robustness because you were using a dynamic pricing policy so there are a lot of different ways to give these kinds of robustness results and | 2,108 | 2,124 | https://www.youtube.com/watch?v=lDLqrsye-rQ&t=2108s | Dynamic Pricing in Ride-Sharing Platforms | |
lDLqrsye-rQ | again in the revenue management literature it usually involves taking the second-order limit like looking at a fusion limit of the system and there those are nice but but definitely technically complex what we want to do is take maybe a more of a robust optimization viewpoint where we basically said let's ask can we get sort of dynamic pricing to be near optimal | 2,124 | 2,142 | https://www.youtube.com/watch?v=lDLqrsye-rQ&t=2124s | Dynamic Pricing in Ride-Sharing Platforms | |
lDLqrsye-rQ | across a wide range of system parameters okay so again I'll just tell you that the result in pictures so here what I'm doing is I'm picking one of the parameters let's say the exoticness arrival rate of passengers and of you know app opens and what I'm plotting here is this is the throughput I would get if regardless of what the you know for each value the system parameter I | 2,142 | 2,164 | https://www.youtube.com/watch?v=lDLqrsye-rQ&t=2142s | Dynamic Pricing in Ride-Sharing Platforms | |
lDLqrsye-rQ | set the optimal static price okay this is the blue curve is what I get if I set the optimal strategy for static price believing that the exogenous rate of customer arrivals was mutant was a 4.0 but in fact it ended up being something different and so yeah right here obviously it's it's optimal but then it really degrades quickly as I move away right well you really want like is the | 2,164 | 2,185 | https://www.youtube.com/watch?v=lDLqrsye-rQ&t=2164s | Dynamic Pricing in Ride-Sharing Platforms | |
lDLqrsye-rQ | difference between these two things now suppose that what I tell myself is okay you know I don't know what me zero is going to be exactly but I think it's gonna be between three point six and four point four so let me take each of those to compute the corresponding static prices for each of those to the optimal static prices and use these two as the two prices in a dynamic pricing | 2,185 | 2,204 | https://www.youtube.com/watch?v=lDLqrsye-rQ&t=2185s | Dynamic Pricing in Ride-Sharing Platforms | |
lDLqrsye-rQ | scheme okay again buried in the background is what threshold do I set to move between these two and I'll just tell you that that we're using the same sort of optimality result that was in the proof to be able to set that threshold between once you give me the two prices I can set the optimal threshold right and what you find is that if you now plot how dynamic | 2,204 | 2,223 | https://www.youtube.com/watch?v=lDLqrsye-rQ&t=2204s | Dynamic Pricing in Ride-Sharing Platforms | |
lDLqrsye-rQ | pricing does using these two prices the two prices from the extremes then yeah it degrades badly outside of that uncertainty set but inside the uncertainty set and what we can show is that dynamic pricing always gets you at least the linear interpolation between these two optimal values okay and at least in the numerical experiments we've done that tends to be quite good this | 2,223 | 2,242 | https://www.youtube.com/watch?v=lDLqrsye-rQ&t=2223s | Dynamic Pricing in Ride-Sharing Platforms | |
lDLqrsye-rQ | the the green curve is is concave and all the experiments we've looked at so far numerical experiments so basically the point is the result we have is something which characterizes the robustness of dynamic pricing through this notion of an uncertainty set over system parameters and says that you always do at least as well as the linear interpolation from the endpoints of your | 2,242 | 2,260 | https://www.youtube.com/watch?v=lDLqrsye-rQ&t=2242s | Dynamic Pricing in Ride-Sharing Platforms | |
lDLqrsye-rQ | uncertainty set and this kind of a technical statement of that okay so let me conclude so a bunch of different things that we were trying to do in this in this work and so some things I didn't you know managed to get to network modeling with multiple regions when I say our main insights generalize I mean they generalize sort of to the extent that we're you know | 2,260 | 2,281 | https://www.youtube.com/watch?v=lDLqrsye-rQ&t=2260s | Dynamic Pricing in Ride-Sharing Platforms | |
lDLqrsye-rQ | able to characterize this difference between static and dynamic pricing we haven't accounted for ETA sort of in the way that David asked about right aggregate welfare is something like I said numerically we get very similar insights but but we're trying to work the theory out there and I think it really gets interesting when you start changing you know when you start asking | 2,281 | 2,297 | https://www.youtube.com/watch?v=lDLqrsye-rQ&t=2281s | Dynamic Pricing in Ride-Sharing Platforms | |
lDLqrsye-rQ | you know much more foundational design questions so one thing that that I think Chris even pointed out is that you know you can imagine showing drivers these heat maps where we're saying like here is a place where there's there's more or less demand available we have some model inside the queueing model we've we've come up with some nice sort of tractable ways to deal with this but extending it | 2,297 | 2,320 | https://www.youtube.com/watch?v=lDLqrsye-rQ&t=2297s | Dynamic Pricing in Ride-Sharing Platforms | |
lDLqrsye-rQ | then to add in the strategic the strategic component has not been so easy but I think that again this is a really important direction to take the work it's be structure changing the percentage we talked about already and finally I think that there's sort of changing the matching algorithm there's something which has really not discussed a lot if you ask you know uber or lyft | 2,320 | 2,337 | https://www.youtube.com/watch?v=lDLqrsye-rQ&t=2320s | Dynamic Pricing in Ride-Sharing Platforms | |
lDLqrsye-rQ | I'm sure they would say that they want it to be fairly transparent so you're match to the nearest driver there's all kinds of really good reasons why you might want to manage inventory very differently across the network especially if you for those of you that were here for the industry the reverse field trip day you know they were talking about this sort of you know | 2,337 | 2,353 | https://www.youtube.com/watch?v=lDLqrsye-rQ&t=2337s | Dynamic Pricing in Ride-Sharing Platforms | |
lDLqrsye-rQ | tessellation of the earth into smaller regions than what they've been using before and once you start doing that I absolutely think you would want your match algorithm to occasionally pick people from adjacent regions you know depending on you know or another example this would be the Chris on Monday mentioned that uber wants to be able to accommodate driver preferences it use | 2,353 | 2,371 | https://www.youtube.com/watch?v=lDLqrsye-rQ&t=2353s | Dynamic Pricing in Ride-Sharing Platforms | |
lDLqrsye-rQ | either Chris or last week that if a driver says hey I want to be able to be get back to the East Bay in an hour I'm gonna accommodate well that's gonna change the match algorithm you're not going to give it to the nearest driver necessarily and I think this is again one of these things with sort of geographic matching you would have to have a good queueing model and you would | 2,371 | 2,386 | https://www.youtube.com/watch?v=lDLqrsye-rQ&t=2371s | Dynamic Pricing in Ride-Sharing Platforms | |
pfFyZY1RPZU | once it is set maybe high level vision show some of the ideas I think are the big ideas in future learning I think the agenda of deep learning as the idea of using brain simulations to make learning algorithms might better than easy to use and also make revolution advances in machine learning and AI so come back to this later but you know once upon a time I guess when I | 0 | 29 | https://www.youtube.com/watch?v=pfFyZY1RPZU&t=0s | Andrew Ng: "Deep Learning, Self-Taught Learning and Unsupervised Feature Learning" | |
pfFyZY1RPZU | was in high school I think I joined the field of machine learning because I want to work on AI but somehow that got lost and instead of actually doing AI we wound up spending our lives doing curve fitting which is not what I signed up to do uh and and deep learning was for the first time in many years made me think about the bigger dreams again I should come back and say a bit more about that | 29 | 47 | https://www.youtube.com/watch?v=pfFyZY1RPZU&t=29s | Andrew Ng: "Deep Learning, Self-Taught Learning and Unsupervised Feature Learning" | |
pfFyZY1RPZU | and and again I would say you know the sort of vision and ideas on a share is really not mine but as I think shared by large community including you know young Jeff Fenton yoshua bengio and many others that you hear from in the next couple weeks what about computers do with our data right we want to talk with images and label them lock of audio listen to audio | 47 | 66 | https://www.youtube.com/watch?v=pfFyZY1RPZU&t=47s | Andrew Ng: "Deep Learning, Self-Taught Learning and Unsupervised Feature Learning" | |
pfFyZY1RPZU | and do speech recognition have text and do stuff with text and it turns out that machine learning is our best shot and most of these applications today but it is very difficult to get these applications work right so while back i ôll some of my students at stanford to use like a state-of-the-art computer vision algorithm to to write the motorcycle detector and this was the | 66 | 93 | https://www.youtube.com/watch?v=pfFyZY1RPZU&t=66s | Andrew Ng: "Deep Learning, Self-Taught Learning and Unsupervised Feature Learning" | |
pfFyZY1RPZU | resulting god and this is typical in computer vision right so um well even though learning algorithms works each of those lines is like a you know six months to two years of work for a team of engineers and and we like these algorithms to be less work to build and also maybe perform better so let me start to explain some of these ideas using computer vision but and then I | 93 | 125 | https://www.youtube.com/watch?v=pfFyZY1RPZU&t=93s | Andrew Ng: "Deep Learning, Self-Taught Learning and Unsupervised Feature Learning" | |
pfFyZY1RPZU | will talk about about audio and apply these albums other modalities as well so why is this problem hard right so obviously a motorcycle how on earth could a computer fail to recognize what this is zooming into small part of the image zooming into whether little red square is where you and I see a motorcycle the computer sees this so the computer vision problem is to | 125 | 148 | https://www.youtube.com/watch?v=pfFyZY1RPZU&t=125s | Andrew Ng: "Deep Learning, Self-Taught Learning and Unsupervised Feature Learning" | |
pfFyZY1RPZU | look at all those pixel intensity values and tell you that all those numbers represent the exhaust pipe of a motorcycle seems like you need a very complicated function to do that and how do we do this so machine learning you know machine learning guys like me say oh just feed the data to the learning algorithm and let the learning algorithm do its job right when I teach my machine | 148 | 171 | https://www.youtube.com/watch?v=pfFyZY1RPZU&t=148s | Andrew Ng: "Deep Learning, Self-Taught Learning and Unsupervised Feature Learning" | |
pfFyZY1RPZU | learning cause I draw pictures like this and this is just not how it works so let's pick a couple pixels and let's plot some examples right so take that image there and because pixel one is relatively dark and pixel two is relatively bright that image you know it has has that position in this figure now let's take a different example a different motorcycle image has a this | 171 | 196 | https://www.youtube.com/watch?v=pfFyZY1RPZU&t=171s | Andrew Ng: "Deep Learning, Self-Taught Learning and Unsupervised Feature Learning" | |
pfFyZY1RPZU | has a bright two pixel one in the darker pixel too so that second image gets passed a different location and then let's do this for a few negative examples as well no motorcycles and what you find is that if you plot a set of positive and negative motorcycle and non motorcycle images that your positive negative examples are extremely jumbled together and so if you feed this data to | 196 | 216 | https://www.youtube.com/watch?v=pfFyZY1RPZU&t=196s | Andrew Ng: "Deep Learning, Self-Taught Learning and Unsupervised Feature Learning" | |
pfFyZY1RPZU | you know certainly a linear classifier it doesn't work so what is done is that the machine learning is that we want to be nice if you could come up with what's called a feature representation if you could write a piece of code that tells you does this image have handlebars in it does this image have tires or wheels in it and if you could do that then your data looks more like this on the lower | 216 | 244 | https://www.youtube.com/watch?v=pfFyZY1RPZU&t=216s | Andrew Ng: "Deep Learning, Self-Taught Learning and Unsupervised Feature Learning" | |
pfFyZY1RPZU | right and it then becomes easy much easier for say a linear classifier like a swivel vector machine the logistic regression to distinguish the motorcycles from the banal motor signals right but the story goes on so will this in this illustrative example or saying well whether we could write a piece of code to tell us that their handlebars and wheels but we don't actually know | 244 | 264 | https://www.youtube.com/watch?v=pfFyZY1RPZU&t=244s | Andrew Ng: "Deep Learning, Self-Taught Learning and Unsupervised Feature Learning" | |
pfFyZY1RPZU | how to do that and so in computer vision what is done is actually the following this is how people actually come up with features in computer vision this kind of notional illustrative example but this is what I wanna do when I take my motorcycle I make I'm going to detect edges at four different orientations so look for vertical edges horizontal edges 45-degree ages 135 | 264 | 286 | https://www.youtube.com/watch?v=pfFyZY1RPZU&t=264s | Andrew Ng: "Deep Learning, Self-Taught Learning and Unsupervised Feature Learning" | |
pfFyZY1RPZU | degree edges and then what this number or point seven and the upper right means right that number is saying that the density of vertical edges in the upper right hand quadrant of my image is 0.7 and what and what this number down here says is that the density of horizontal edges you know in the lower right hand quadrant of my image is 0.5 and in case you're getting the sense that sort of | 286 | 319 | https://www.youtube.com/watch?v=pfFyZY1RPZU&t=286s | Andrew Ng: "Deep Learning, Self-Taught Learning and Unsupervised Feature Learning" | |
pfFyZY1RPZU | like oh my god what on earth is going on there this seems hardly complicated how interrupts it will come up with this piece of code you know that's that's that's the point and sadly this is the way that a lot of computer vision is done today so we'll probably this notion of a feature representation is pervasive throughout machine learning in fact I guess I live in I live in Silicon Valley | 319 | 340 | https://www.youtube.com/watch?v=pfFyZY1RPZU&t=319s | Andrew Ng: "Deep Learning, Self-Taught Learning and Unsupervised Feature Learning" | |
pfFyZY1RPZU | and if you walk around Silicon Valley and look at what where people are spending all the engineering time is often in coming up with these feature representations so let's let's look what's delve deeper right so where do these features come from um since they're the primary lens through which our algorithms see the world this gives them a certain importance right so how | 340 | 361 | https://www.youtube.com/watch?v=pfFyZY1RPZU&t=340s | Andrew Ng: "Deep Learning, Self-Taught Learning and Unsupervised Feature Learning" | |
pfFyZY1RPZU | about computer vision oh and then facts are interesting and in fact this notion of feature representations is pervasive you know for vision audio text even other applications so what do you get the features from in computer vision the state of the art answer for where the features come from is that teams of tens hundreds or teams of some of tens hundreds or maybe thousands of computer | 361 | 383 | https://www.youtube.com/watch?v=pfFyZY1RPZU&t=361s | Andrew Ng: "Deep Learning, Self-Taught Learning and Unsupervised Feature Learning" | |
pfFyZY1RPZU | vision researchers have spent decades of their lives hand engineering features for computer vision the figure on the upper left is a figure that I took from the stiff paper the stiff paper is the single most highly cited paper in computer vision like fifteen years and I read the paper maybe about five times now and I still have no idea what it's doing right this is | 383 | 408 | https://www.youtube.com/watch?v=pfFyZY1RPZU&t=383s | Andrew Ng: "Deep Learning, Self-Taught Learning and Unsupervised Feature Learning" | |
pfFyZY1RPZU | something so complex piece of code that David loathes good friend David will tell you this himself it took David literally ten years I'm knocking he's he'll say 10 years himself of you know filling with pieces of the code in order to come up with the SIP feature which works pretty well but you know you have to ask is there a better way to design features than this | 408 | 429 | https://www.youtube.com/watch?v=pfFyZY1RPZU&t=408s | Andrew Ng: "Deep Learning, Self-Taught Learning and Unsupervised Feature Learning" | |
pfFyZY1RPZU | that's vision how about audio same thing right teams of tens hundreds of thousands of audio researchers working on features for audio ever CC is shown on the upper right that's actually a pretty clever surprisingly hard to beat but again you know honestly to this day I have a hard time understanding what some bits of the M FCC album are doing and natural language in fact I think | 429 | 453 | https://www.youtube.com/watch?v=pfFyZY1RPZU&t=429s | Andrew Ng: "Deep Learning, Self-Taught Learning and Unsupervised Feature Learning" | |
pfFyZY1RPZU | most of natural language processing text processing today is unapologetically about finding better features so think about pauses right there's a lot of NLP work on parsers um this piece of software that tells you where the noun phrases are in your sentence I mean why on earth do I care where the noun phrases are in my sentences I really don't need software to tell me that the | 453 | 475 | https://www.youtube.com/watch?v=pfFyZY1RPZU&t=453s | Andrew Ng: "Deep Learning, Self-Taught Learning and Unsupervised Feature Learning" | |
pfFyZY1RPZU | only reason we spend so much time working on pauses is because we hope that this will give us useful features to then feed to some later downstream application like anti-spam web search machine translation that we actually care about so common features is difficult time consuming requires expert knowledge and we're working with them applications machine learning you know | 475 | 496 | https://www.youtube.com/watch?v=pfFyZY1RPZU&t=475s | Andrew Ng: "Deep Learning, Self-Taught Learning and Unsupervised Feature Learning" | |
pfFyZY1RPZU | we spent a long time there's a way if you look at apply machine learning where they will walk anew oh the company local people doing apply machine learning this is really what they spend the vast majority of the time on it's coming up with features so can we do better so the next piece in a lot of deep learning there's a like many people in very like many of you I | 496 | 527 | https://www.youtube.com/watch?v=pfFyZY1RPZU&t=496s | Andrew Ng: "Deep Learning, Self-Taught Learning and Unsupervised Feature Learning" | |
pfFyZY1RPZU | tend to treat biological inspiration with a great deal of caution and even a healthy dose of skepticism but for me a lot of the some of my thinking about deep learning has been taken inspiration from biology so I only share of you but you know some some cool cool ideas from really by washing inspiration so turns out there's a fascinating hypothesis that much of human intelligence can be | 527 | 552 | https://www.youtube.com/watch?v=pfFyZY1RPZU&t=527s | Andrew Ng: "Deep Learning, Self-Taught Learning and Unsupervised Feature Learning" | |
pfFyZY1RPZU | explained by a single learning algorithm since cause the one learning our hypothesis let me share with you some evidence for this right so this one's experiment first done on ferrets in MIT on that very piece of brain tissue shown on the slide that's your auditory cortex the way that your understanding my words now is that your ears is routing the sound signal to that piece of great | 552 | 574 | https://www.youtube.com/watch?v=pfFyZY1RPZU&t=552s | Andrew Ng: "Deep Learning, Self-Taught Learning and Unsupervised Feature Learning" | |
pfFyZY1RPZU | brain tissue and this processing the sound and then that's how you you eventually get to understand what I'm saying so neuroscientists did the following experiments which is in cut the wire between the ears and the auditory cortex and do what's called a neural rewiring experiment so that eventually the signal from the eyes gets routed to the auditory cortex it turns | 574 | 598 | https://www.youtube.com/watch?v=pfFyZY1RPZU&t=574s | Andrew Ng: "Deep Learning, Self-Taught Learning and Unsupervised Feature Learning" | |
pfFyZY1RPZU | out if you do this that great piece of brain tissue learns to see and this is the word see this has been replicated in multiple labs on four species of animals and these animals can quote see in every single sense of the word that I know how to use the word see these animals they can do visual discrimination talks we can look at things and make correct decisions based on you know an image in | 598 | 619 | https://www.youtube.com/watch?v=pfFyZY1RPZU&t=598s | Andrew Ng: "Deep Learning, Self-Taught Learning and Unsupervised Feature Learning" | |
pfFyZY1RPZU | front of them using that rare piece of brain tissue another example this rare piece of brain tissue is your somatosensory cortex is responsible for your sense of touch do a similar neural rewiring experiment and your somatosensory cortex Lucy um so more generally this is idea that if the same physical piece of brain tissue right the same physical bit of your brain can process sight or sound or | 619 | 646 | https://www.youtube.com/watch?v=pfFyZY1RPZU&t=619s | Andrew Ng: "Deep Learning, Self-Taught Learning and Unsupervised Feature Learning" | |
pfFyZY1RPZU | touch or maybe even other things then maybe there's a single learning algorithm they can process sight or sound or touch or maybe other things and that it can you know discover some approximation to that learning algorithm when we discover a totally different algorithm but it accomplishes the same thing then that might be a better way to us making progress in AI then hand | 646 | 668 | https://www.youtube.com/watch?v=pfFyZY1RPZU&t=646s | Andrew Ng: "Deep Learning, Self-Taught Learning and Unsupervised Feature Learning" |
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