Being Optimistic to Be Conservative: Quickly Learning a CVaR Policy

Being Optimistic to Be Conservative: Quickly Learning a CV aR Policy Ramtin Keramati 1, Christoph Dann 2, Alex T amkin 3, Emma Brunskill 3 1 Institute of Computational and Mathematical Engineering (ICME), Stanford University, California, USA 2 Machine Learning Department, Carnegie Mellon University, Pittsburgh, Pennsylvania, USA 3 Department of Computer Science, Stanford University, California, USA {keramati,atamkin,ebrun } @cs.stanford.edu Abstract While maximizing expected return is the goal in most reinforcement learning approaches, risk-sensitive objectives such as conditional value at risk (CV aR) are more suitable for many high-stakes applications. However, relatively little is known about how to explore to quickly learn policies with good CV aR. In this paper, we present the first algorithm for sample-efficient learning of CV aR-optimal policies in Markov decision processes based on the optimism in the face of uncertainty principle. This method relies on a novel optimistic version of the distributional Bellman operator that moves probability mass from the lower to the upper tail of the return distribution. We prove asymptotic convergence and optimism of this operator for the tabular policy evaluation case. We further demonstrate that our algorithm finds CV aR-optimal policies substantially faster than existing baselines in several simulated environments with discrete and continuous state spaces. Introduction A key goal in reinforcement learning (RL) is to quickly learn to make good decisions by interacting with an environment. In most cases the quality of the decision policy is evaluated with respect to its expected (discounted) sum of rewards. However, in many interesting cases, it is important to consider the full distributions over the potential sum of rewards, and the desired objective may be a risk-sensitive measure of this distribution. For example, a patient undergoing a surgery for a knee replacement will (hopefully) only experience that procedure once or twice, and may will be interested in the distribution of potential results for a single procedure, rather than what may happen on average if he or she were to undertake that procedure hundreds of time. Finance and (machine) control are other cases where interest in risk-sensitive outcomes are common. A popular risk-sensitive measure of a distribution of outcomes is the Conditional V alue at Risk (CV aR) (Artzner et al. 1999). Intuitively, CV aR is the expected reward in the worst α -fraction of outcomes, and has seen extensive use in financial portfolio optimization (Zhu and Fukushima 2009), often under the name "expected shortfall".