Yuhao Wang

Yifan Lin, Yuhao Wang, Enlu Zhou · gatech

In this paper we consider the contextual multi-armed bandit problem for linear payoffs under a risk-averse criterion. At each round, contexts are revealed for each arm, and the decision maker chooses one arm to pull and receives the corresponding reward. In particular, we consider mean-variance as the risk criterion, and the best arm is the one with the largest mean-variance reward. We apply the Thompson Sampling algorithm for the disjoint model, and provide a comprehensive regret analysis for a variant of the proposed algorithm. For $T$ rounds, $K$ actions, and $d$-dimensional feature vectors, we prove a regret bound of $O((1+ρ+\frac{1}ρ) d\ln T \ln \frac{K}δ\sqrt{d K T^{1+2ε} \ln \frac{K}δ \frac{1}ε})$ that holds with probability $1-δ$ under the mean-variance criterion with risk tolerance $ρ$, for any $0<ε<\frac{1}{2}$, $0<δ<1$. The empirical performance of our proposed algorithms is demonstrated via a portfolio selection problem.

Yuhao Wang, Enlu Zhou

We consider a robust reinforcement learning problem, where a learning agent learns from a simulated training environment. To account for the model mis-specification between this training environment and the real environment due to lack of data, we adopt a formulation of Bayesian risk MDP (BRMDP) with infinite horizon, which uses Bayesian posterior to estimate the transition model and impose a risk functional to account for the model uncertainty. Observations from the real environment that is out of the agent's control arrive periodically and are utilized by the agent to update the Bayesian posterior to reduce model uncertainty. We theoretically demonstrate that BRMDP balances the trade-off between robustness and conservativeness, and we further develop a multi-stage Bayesian risk-averse Q-learning algorithm to solve BRMDP with streaming observations from real environment. The proposed algorithm learns a risk-averse yet optimal policy that depends on the availability of real-world observations. We provide a theoretical guarantee of strong convergence for the proposed algorithm.