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A Distributional Perspective on Reinforcement Learning

2017-07-21ICML 2017Code Available1· sign in to hype

Marc G. Bellemare, Will Dabney, Rémi Munos

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Abstract

In this paper we argue for the fundamental importance of the value distribution: the distribution of the random return received by a reinforcement learning agent. This is in contrast to the common approach to reinforcement learning which models the expectation of this return, or value. Although there is an established body of literature studying the value distribution, thus far it has always been used for a specific purpose such as implementing risk-aware behaviour. We begin with theoretical results in both the policy evaluation and control settings, exposing a significant distributional instability in the latter. We then use the distributional perspective to design a new algorithm which applies Bellman's equation to the learning of approximate value distributions. We evaluate our algorithm using the suite of games from the Arcade Learning Environment. We obtain both state-of-the-art results and anecdotal evidence demonstrating the importance of the value distribution in approximate reinforcement learning. Finally, we combine theoretical and empirical evidence to highlight the ways in which the value distribution impacts learning in the approximate setting.

Tasks

Benchmark Results

DatasetModelMetricClaimedVerifiedStatus
Atari 2600 AlienC51 noopScore3,166—Unverified
Atari 2600 AmidarC51 noopScore1,735—Unverified
Atari 2600 AssaultC51 noopScore7,203—Unverified
Atari 2600 AsterixC51 noopScore406,211—Unverified
Atari 2600 AsteroidsC51 noopScore1,516—Unverified
Atari 2600 AtlantisC51 noopScore841,075—Unverified
Atari 2600 Bank HeistC51 noopScore976—Unverified
Atari 2600 Battle ZoneC51 noopScore28,742—Unverified
Atari 2600 Beam RiderC51 noopScore14,074—Unverified
Atari 2600 BerzerkC51 noopScore1,645—Unverified
Atari 2600 BowlingC51 noopScore81.8—Unverified
Atari 2600 BoxingC51 noopScore97.8—Unverified
Atari 2600 BreakoutC51 noopScore748—Unverified
Atari 2600 CentipedeC51 noopScore9,646—Unverified
Atari 2600 Chopper CommandC51 noopScore15,600—Unverified
Atari 2600 Crazy ClimberC51 noopScore179,877—Unverified
Atari 2600 Demon AttackC51 noopScore130,955—Unverified
Atari 2600 Double DunkC51 noopScore2.5—Unverified
Atari 2600 EnduroC51 noopScore3,454—Unverified
Atari 2600 Fishing DerbyC51 noopScore8.9—Unverified
Atari 2600 FreewayC51 noopScore33.9—Unverified
Atari 2600 FrostbiteC51 noopScore3,965—Unverified
Atari 2600 GopherC51 noopScore33,641—Unverified
Atari 2600 GravitarC51 noopScore440—Unverified
Atari 2600 HEROC51 noopScore38,874—Unverified
Atari 2600 Ice HockeyC51 noopScore-3.5—Unverified
Atari 2600 James BondC51 noopScore1,909—Unverified
Atari 2600 KangarooC51 noopScore12,853—Unverified
Atari 2600 KrullC51 noopScore9,735—Unverified
Atari 2600 Kung-Fu MasterC51 noopScore48,192—Unverified
Atari 2600 Ms. PacmanC51 noopScore3,415—Unverified
Atari 2600 Name This GameC51 noopScore12,542—Unverified
Atari 2600 PongC51 noopScore20.9—Unverified
Atari 2600 Private EyeC51 noopScore15,095—Unverified
Atari 2600 Q*BertC51 noopScore23,784—Unverified
Atari 2600 River RaidC51 noopScore17,322—Unverified
Atari 2600 Road RunnerC51 noopScore55,839—Unverified
Atari 2600 RobotankC51 noopScore52.3—Unverified
Atari 2600 SeaquestC51 noopScore266,434—Unverified
Atari 2600 Space InvadersC51 noopScore5,747—Unverified
Atari 2600 Star GunnerC51 noopScore49,095—Unverified
Atari 2600 TennisC51 noopScore23.1—Unverified
Atari 2600 Time PilotC51 noopScore8,329—Unverified
Atari 2600 TutankhamC51 noopScore280—Unverified
Atari 2600 Up and DownC51 noopScore15,612—Unverified
Atari 2600 VentureC51 noopScore1,520—Unverified
Atari 2600 Video PinballC51 noopScore949,604—Unverified
Atari 2600 Wizard of WorC51 noopScore9,300—Unverified
Atari 2600 ZaxxonC51 noopScore10,513—Unverified

Reproductions