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

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

A Geometric Proof of Calibration

We provide yet another proof of the existence of calibrated forecasters; it has two merits. First, it is valid for an arbitrary finite number of outcomes. Second, it is short and simple and it follows from a direct application of Blackwell's approachability theorem to carefully chosen vector-valued payoff function and convex target set. Our proof captures the essence of existing proofs based on approachability (e.g., the proof by Foster, 1999 in case of binary outcomes) and highlights the intrinsic connection between approachability and calibration