2019

Online Convex Optimization in Adversarial Markov Decision Processes

Rosenberg, Aviv, Mansour, Yishay

Understand

We consider online learning in episodic loop-free Markov decision processes (MDPs), where the loss function can change arbitrarily between episodes, and the transition function is not known to the learner.

  • We show $\tilde{O}(L|X|\sqrt{|A|T})$ regret bound, where $T$ is the number of episodes, $X$ is the state space, $A$ is the action space, and $L$ is the length of each episode.
  • Our online algorithm is implemented using entropic regularization methodology, which allows to extend the original adversarial MDP model to handle convex performance criteria (different ways to aggregate the losses of a single episode) , as well as improve previous regret bounds.

Built on

  • Markov Decision Processes: Discrete Stochastic Dynamic Programming

    Puterman, M. L · 1994

    Earlier work this paper cites.

  • Efficient algorithms for online decision problems

    Kalai, A. and Vempala, S · 2003

    Earlier work this paper cites.

  • Convex Optimization

    Boyd, S. and Vandenberghe, L · 2004

    Earlier work this paper cites.

  • Online Markov Decision Processes

    Even-Dar, E., Kakade, S. M., and Mansour, Y · 2004

    Earlier work this paper cites.

  • Prediction, learning, and games

    Cesa-Bianchi, N. and Lugosi, G · 2006

    Earlier work this paper cites.

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    Bartlett, P. L. and Tewari, A · 2009

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  • Markov Decision Processes with arbitrary reward processes

    Yu, J. Y., Mannor, S., and Shimkin, N · 2009

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  • The online loop-free stochastic shortest-path problem

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  • The adversarial stochastic shortest path problem with unknown transition probabilities

    Neu, G., György, A., and Szepesvári, C · 2012

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Then

  • Online learning and online convex optimization

    Shalev-Shwartz, S · 2012

    Later among the works it cites.

  • Online learning in episodic markovian decision processes by relative entropy policy search

    Zimin, A. and Neu, G · 2013

    Later among the works it cites.

  • Online Markov Decision Processes under bandit feedback

    Neu, G., György, A., Szepesvári, C., and Antos, A · 2014

    Later among the works it cites.

  • Minimax regret bounds for reinforcement learning

    Azar, M. G., Osband, I., and Munos, R · 2017

    Later among the works it cites.

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