autogen/website/blog/2023-04-21-LLM-tuning-math/index.md
Analysis and Discussion  While gpt-3.5-turbo demonstrates competitive accuracy with voted answers in relatively easy algebra problems under the same inference budget, gpt-4 is a better choice for the most difficult problems. In general, through parameter tuning and model selection, we can identify the opportunity to save the expensive model for more challenging tasks, and improve the overall effectiveness of a budget-constrained system.  There are many other alternative ways of solving math problems, which we have not covered in this blog post. When there are choices beyond the inference parameters, they can be generally tuned via [`flaml.tune`](https://microsoft.github.io/FLAML/docs/Use-Cases/Tune-User-Defined-Function).  The need for model selection, parameter tuning and cost saving is not specific to the math problems. The [Auto-GPT](https://github.com/Significant-Gravitas/Auto-GPT) project is an example where high cost can easily prevent a generic complex task to be accomplished as it needs many LLM inference calls. 