Mean-Variance Optimization in Markov Decision Processes

We consider finite horizon Markov decision processes under performance measures that involve both the mean and the variance of the cumulative reward. We show that either randomized or history-based policies can improve performance. We prove that the complexity of computing a policy that maximizes the mean reward under a variance constraint is NP-hard for some cases, and strongly NP-hard for others. We finally offer pseudopolynomial exact and approximation algorithms.Comment: A full version of an ICML 2011 pape

Reinforcement Learning for the Unit Commitment Problem

In this work we solve the day-ahead unit commitment (UC) problem, by formulating it as a Markov decision process (MDP) and finding a low-cost policy for generation scheduling. We present two reinforcement learning algorithms, and devise a third one. We compare our results to previous work that uses simulated annealing (SA), and show a 27% improvement in operation costs, with running time of 2.5 minutes (compared to 2.5 hours of existing state-of-the-art).Comment: Accepted and presented in IEEE PES PowerTech, Eindhoven 2015, paper ID 46273

From Bandits to Experts: On the Value of Side-Observations

We consider an adversarial online learning setting where a decision maker can choose an action in every stage of the game. In addition to observing the reward of the chosen action, the decision maker gets side observations on the reward he would have obtained had he chosen some of the other actions. The observation structure is encoded as a graph, where node i is linked to node j if sampling i provides information on the reward of j. This setting naturally interpolates between the well-known "experts" setting, where the decision maker can view all rewards, and the multi-armed bandits setting, where the decision maker can only view the reward of the chosen action. We develop practical algorithms with provable regret guarantees, which depend on non-trivial graph-theoretic properties of the information feedback structure. We also provide partially-matching lower bounds.Comment: Presented at the NIPS 2011 conferenc