Thompson Sampling Algorithms for Mean-Variance Bandits
The multi-armed bandit (MAB) problem is a classical learning task that exemplifies the exploration-exploitation tradeoff. However, standard formulations do not take into account {\em risk}. In online decision making systems, risk is a primary concern. In this regard, the mean-variance risk measure is one of the most common objective functions. Existing algorithms for mean-variance optimization in the context of MAB problems have unrealistic assumptions on the reward distributions. We develop Thompson Sampling-style algorithms for mean-variance MAB and provide comprehensive regret analyses for Gaussian and Bernoulli bandits with fewer assumptions. Our algorithms achieve the best known regret bounds for mean-variance MABs and also attain the information-theoretic bounds in some parameter regimes. Empirical simulations show that our algorithms significantly outperform existing LCB-based algorithms for all risk tolerances.
Code (2)
Tasks
Decision MakingThompson SamplingSimilar Papers 제목 키워드 기반
Variance-Aware Feel-Good Thompson Sampling for Contextual Bandits
Variance-dependent regret bounds have received increasing attention in recent studies on contextual bandits. However, most of these studies are focused on upper confidence bound (UCB)-based bandit algorithms, while sampl…
Noise-Adaptive Thompson Sampling for Linear Contextual Bandits
Linear contextual bandits represent a fundamental class of models with numerous real-world applications, and it is critical to develop algorithms that can effectively manage noise with unknown variance, ensuring provable…
Langevin Monte Carlo for Contextual Bandits
We study the efficiency of Thompson sampling for contextual bandits. Existing Thompson sampling-based algorithms need to construct a Laplace approximation (i.e., a Gaussian distribution) of the posterior distribution, wh…
Multi-Armed BanditsThompson SamplingOptimism Stabilizes Thompson Sampling for Adaptive Inference
Thompson sampling (TS) is widely used for stochastic multi-armed bandits, yet its inferential properties under adaptive data collection are subtle. Classical asymptotic theory for sample means can fail because arm-specif…
Multi-Armed BanditsVariance-sensitive Thompson sampling for generalised linear bandits, revisited
We prove a variance-sensitive regret bound for Thompson sampling in stochastic generalised linear bandits. The argument assumes a warm-up, after which the regret is controlled through using the Gaussian Poincaré inequali…