Risk-Averse Explore-Then-Commit Algorithms for Finite-Time Bandits
This addresses the problem of risk-averse decision-making in finite-time bandit scenarios for applications like online advertising or clinical trials, though it is incremental as it builds on existing explore-then-commit frameworks.
The paper tackles the problem of identifying the best arm in multi-armed bandits for finite-time exploitation by proposing risk-averse explore-then-commit algorithms that aim to select the arm most probable to yield the highest reward, with results including an upper bound for the minimum experiments needed to guarantee regret bounds and improved robustness without hyper-parameters, as verified numerically.
In this paper, we study multi-armed bandit problems in explore-then-commit setting. In our proposed explore-then-commit setting, the goal is to identify the best arm after a pure experimentation (exploration) phase and exploit it once or for a given finite number of times. We identify that although the arm with the highest expected reward is the most desirable objective for infinite exploitations, it is not necessarily the one that is most probable to have the highest reward in a single or finite-time exploitations. Alternatively, we advocate the idea of risk-aversion where the objective is to compete against the arm with the best risk-return trade-off. Then, we propose two algorithms whose objectives are to select the arm that is most probable to reward the most. Using a new notion of finite-time exploitation regret, we find an upper bound for the minimum number of experiments before commitment, to guarantee an upper bound for the regret. As compared to existing risk-averse bandit algorithms, our algorithms do not rely on hyper-parameters, resulting in a more robust behavior in practice, which is verified by the numerical evaluation.