Guaranteed satisficing and finite regret: Analysis of a cognitive
  satisficing value function
  As reinforcement learning algorithms are being applied to increasingly
complicated and realistic tasks, it is becoming increasingly difficult to solve
such problems within a practical time frame. Hence, we focus on a
\textit{satisficing} strategy that looks for an action whose value is above the
aspiration level (analogous to the break-even point), rather than the optimal
action. In this paper, we introduce a simple mathematical model called
risk-sensitive satisficing ($RS$) that implements a satisficing strategy by
integrating risk-averse and risk-prone attitudes under the greedy policy. We
apply the proposed model to the $K$-armed bandit problems, which constitute the
most basic class of reinforcement learning tasks, and prove two propositions.
The first is that $RS$ is guaranteed to find an action whose value is above the
aspiration level. The second is that the regret (expected loss) of $RS$ is
upper bounded by a finite value, given that the aspiration level is set to an
"optimal level" so that satisficing implies optimizing. We confirm the results
through numerical simulations and compare the performance of $RS$ with that of
other representative algorithms for the $K$-armed bandit problems.
