Maillard Sampling: Boltzmann Exploration Done Optimally

• URL: http://arxiv.org/abs/2111.03290v1
• Date: Fri, 5 Nov 2021 06:50:22 GMT
• Title: Maillard Sampling: Boltzmann Exploration Done Optimally
• Authors: Jie Bian, Kwang-Sung Jun
• Abstract summary: This thesis presents a randomized algorithm for the $K$-armed bandit problem. Maillard sampling (MS) computes the probability of choosing each arm in a closed form. We propose a variant of MS called MS$+$ that improves its minimax bound to $sqrtKTlogK$ without losing the optimality.
• Score: 11.282341369957216
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The PhD thesis of Maillard (2013) presents a randomized algorithm for the $K$-armed bandit problem. This less-known algorithm, which we call Maillard sampling (MS), computes the probability of choosing each arm in a closed form, which is useful for counterfactual evaluation from bandit-logged data but was lacking from Thompson sampling, a widely-adopted bandit algorithm in the industry. Motivated by such merit, we revisit MS and perform an improved analysis to show that it achieves both the asymptotical optimality and $\sqrt{KT\log{T}}$ minimax regret bound where $T$ is the time horizon, which matches the standard asymptotically optimal UCB's performance. We then propose a variant of MS called MS$^+$ that improves its minimax bound to $\sqrt{KT\log{K}}$ without losing the asymptotic optimality. MS$^+$ can also be tuned to be aggressive (i.e., less exploration) without losing theoretical guarantees, a unique feature unavailable from existing bandit algorithms. Our numerical evaluation shows the effectiveness of MS$^+$.

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