Papers › Increasing the Action Gap: New Operators for Reinforcement Learning

Increasing the Action Gap: New Operators for Reinforcement Learning

15 Dec 2015arXiv:1512.04860archive 2025-07-28

Marc G. Bellemare, Georg Ostrovski, Arthur Guez, Philip S. Thomas, Rémi Munos

This paper introduces new optimality-preserving operators on Q-functions. We first describe an operator for tabular representations, the consistent Bellman operator, which incorporates a notion of local policy consistency. We show that this local consistency leads to an increase in the action gap at each state; increasing this gap, we argue, mitigates the undesirable effects of approximation and estimation errors on the induced greedy policies. This operator can also be applied to discretized continuous space and time problems, and we provide empirical results evidencing superior performance in this context. Extending the idea of a locally consistent operator, we then derive sufficient conditions for an operator to preserve optimality, leading to a family of operators which includes our consistent Bellman operator. As corollaries we provide a proof of optimality for Baird's advantage learning algorithm and derive other gap-increasing operators with interesting properties. We conclude with an empirical study on 60 Atari 2600 games illustrating the strong potential of these new operators.

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chainer/chainerrl mentioned on GitHubpytorch report
janhuenermann/neurojs mentioned on GitHubtfMIT report

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Tasks

Atari GamesQ-LearningReinforcement LearningReinforcement Learning (RL)reinforcement-learning

Results from the paper archive 2025-07-28

TaskDatasetModelMetricValueRank at snapshotLeaderboardReport
Atari Games Atari 2600 Alien Persistent AL Score 5699.81 #16 of 49 Archive leaderboard report
Atari Games Atari 2600 Alien Advantage Learning Score 4990.91 #18 of 49 Archive leaderboard report
Atari Games Atari 2600 Amidar Advantage Learning Score 1557.43 #16 of 48 Archive leaderboard report
Atari Games Atari 2600 Amidar Persistent AL Score 1451.65 #18 of 48 Archive leaderboard report
Atari Games Atari 2600 Assault Advantage Learning Score 3661.51 #33 of 45 Archive leaderboard report
Atari Games Atari 2600 Assault Persistent AL Score 3304.33 #36 of 45 Archive leaderboard report
Atari Games Atari 2600 Asterix Persistent AL Score 19564.9 #28 of 49 Archive leaderboard report
Atari Games Atari 2600 Asterix Advantage Learning Score 12852.08 #36 of 49 Archive leaderboard report
Atari Games Atari 2600 Asteroids Advantage Learning Score 1924.42 #28 of 43 Archive leaderboard report
Atari Games Atari 2600 Asteroids Persistent AL Score 1673.52 #30 of 43 Archive leaderboard report
Atari Games Atari 2600 Atlantis Persistent AL Score 1465250 #8 of 42 Archive leaderboard report
Atari Games Atari 2600 Atlantis Advantage Learning Score 553591.67 #25 of 42 Archive leaderboard report
Atari Games Atari 2600 Bank Heist Persistent AL Score 874.99 #32 of 45 Archive leaderboard report
Atari Games Atari 2600 Bank Heist Advantage Learning Score 633.63 #33 of 45 Archive leaderboard report
Atari Games Atari 2600 Battle Zone Persistent AL Score 34583.07 #20 of 47 Archive leaderboard report
Atari Games Atari 2600 Battle Zone Advantage Learning Score 28789.29 #27 of 47 Archive leaderboard report
Atari Games Atari 2600 Beam Rider Persistent AL Score 13145.34 #29 of 49 Archive leaderboard report
Atari Games Atari 2600 Beam Rider Advantage Learning Score 10054.58 #32 of 49 Archive leaderboard report
Atari Games Atari 2600 Berzerk Persistent AL Score 1328.25 #22 of 39 Archive leaderboard report
Atari Games Atari 2600 Berzerk Advantage Learning Score 747.26 #34 of 39 Archive leaderboard report
Atari Games Atari 2600 Bowling Persistent AL Score 71.59 #18 of 44 Archive leaderboard report
Atari Games Atari 2600 Bowling Advantage Learning Score 57.41 #26 of 44 Archive leaderboard report
Atari Games Atari 2600 Boxing Persistent AL Score 94.3 #25 of 45 Archive leaderboard report
Atari Games Atari 2600 Boxing Advantage Learning Score 93.94 #26 of 45 Archive leaderboard report
Atari Games Atari 2600 Breakout Persistent AL Score 431.89 #23 of 58 Archive leaderboard report
Atari Games Atari 2600 Breakout Advantage Learning Score 425.32 #24 of 58 Archive leaderboard report
Atari Games Atari 2600 Centipede Persistent AL Score 4539.55 #34 of 45 Archive leaderboard report
Atari Games Atari 2600 Centipede Advantage Learning Score 4225.18 #36 of 45 Archive leaderboard report
Atari Games Atari 2600 Chopper Command Persistent AL Score 5734.93 #30 of 45 Archive leaderboard report
Atari Games Atari 2600 Chopper Command Advantage Learning Score 5431.36 #31 of 45 Archive leaderboard report
Atari Games Atari 2600 Crazy Climber Persistent AL Score 130002.71 #25 of 49 Archive leaderboard report
Atari Games Atari 2600 Crazy Climber Advantage Learning Score 123410.71 #29 of 49 Archive leaderboard report
Atari Games Atari 2600 Defender Persistent AL Score 32038.93 #20 of 21 Archive leaderboard report
Atari Games Atari 2600 Defender Advantage Learning Score 30643.59 #21 of 21 Archive leaderboard report
Atari Games Atari 2600 Demon Attack Persistent AL Score 70908.17 #25 of 46 Archive leaderboard report
Atari Games Atari 2600 Demon Attack Advantage Learning Score 27153.48 #35 of 46 Archive leaderboard report
Atari Games Atari 2600 Double Dunk Advantage Learning Score -0.15 #39 of 43 Archive leaderboard report
Atari Games Atari 2600 Double Dunk Persistent AL Score -2.51 #40 of 43 Archive leaderboard report
Atari Games Atari 2600 Elevator Action Persistent AL Score 29100 #1 of 3 Archive leaderboard report
Atari Games Atari 2600 Elevator Action Advantage Learning Score 27088.89 #2 of 3 Archive leaderboard report
Atari Games Atari 2600 Enduro Persistent AL Score 1343.1 #25 of 48 Archive leaderboard report
Atari Games Atari 2600 Enduro Advantage Learning Score 1252.7 #26 of 48 Archive leaderboard report
Atari Games Atari 2600 Fishing Derby Persistent AL Score 28.13 #24 of 44 Archive leaderboard report
Atari Games Atari 2600 Fishing Derby Advantage Learning Score 21.32 #27 of 44 Archive leaderboard report
Atari Games Atari 2600 Freeway Persistent AL Score 32.3 #26 of 59 Archive leaderboard report
Atari Games Atari 2600 Freeway Advantage Learning Score 31.72 #28 of 59 Archive leaderboard report
Atari Games Atari 2600 Frostbite Persistent AL Score 3248.96 #25 of 53 Archive leaderboard report
Atari Games Atari 2600 Frostbite Advantage Learning Score 2305.82 #30 of 53 Archive leaderboard report
Atari Games Atari 2600 Gopher Advantage Learning Score 11912.68 #29 of 43 Archive leaderboard report
Atari Games Atari 2600 Gopher Persistent AL Score 10611.81 #30 of 43 Archive leaderboard report
Atari Games Atari 2600 Gravitar Persistent AL Score 446.92 #34 of 53 Archive leaderboard report
Atari Games Atari 2600 Gravitar Advantage Learning Score 417.65 #37 of 53 Archive leaderboard report
Atari Games Atari 2600 HERO Advantage Learning Score 24788.86 #20 of 44 Archive leaderboard report
Atari Games Atari 2600 HERO Persistent AL Score 24175.79 #21 of 44 Archive leaderboard report
Atari Games Atari 2600 Ice Hockey Persistent AL Score -0.25 #37 of 43 Archive leaderboard report
Atari Games Atari 2600 Ice Hockey Advantage Learning Score -1.24 #38 of 43 Archive leaderboard report
Atari Games Atari 2600 James Bond Advantage Learning Score 848.46 #24 of 45 Archive leaderboard report
Atari Games Atari 2600 James Bond Persistent AL Score 772.09 #27 of 45 Archive leaderboard report
Atari Games Atari 2600 Kangaroo Persistent AL Score 11478.46 #21 of 47 Archive leaderboard report
Atari Games Atari 2600 Kangaroo Advantage Learning Score 10809.16 #24 of 47 Archive leaderboard report
Atari Games Atari 2600 Krull Advantage Learning Score 9548.92 #22 of 45 Archive leaderboard report
Atari Games Atari 2600 Krull Persistent AL Score 8689.81 #24 of 45 Archive leaderboard report
Atari Games Atari 2600 Kung-Fu Master Persistent AL Score 34650.91 #25 of 43 Archive leaderboard report
Atari Games Atari 2600 Kung-Fu Master Advantage Learning Score 32182.99 #30 of 43 Archive leaderboard report
Atari Games Atari 2600 Montezuma's Revenge Persistent AL Score 1.72 #40 of 50 Archive leaderboard report
Atari Games Atari 2600 Montezuma's Revenge Advantage Learning Score 0.42 #41 of 50 Archive leaderboard report
Atari Games Atari 2600 Ms. Pacman Advantage Learning Score 4065.8 #22 of 47 Archive leaderboard report
Atari Games Atari 2600 Ms. Pacman Persistent AL Score 3917.55 #24 of 47 Archive leaderboard report
Atari Games Atari 2600 Name This Game Advantage Learning Score 11025.26 #27 of 43 Archive leaderboard report
Atari Games Atari 2600 Name This Game Persistent AL Score 10431.33 #31 of 43 Archive leaderboard report
Atari Games Atari 2600 Phoenix Advantage Learning Score 22038.27 #16 of 21 Archive leaderboard report
Atari Games Atari 2600 Phoenix Persistent AL Score 14495.56 #18 of 21 Archive leaderboard report
Atari Games Atari 2600 Pitfall! Advantage Learning Score 0 #10 of 23 Archive leaderboard report
Atari Games Atari 2600 Pong Persistent AL Score 19.76 #31 of 52 Archive leaderboard report
Atari Games Atari 2600 Pong Advantage Learning Score 19.66 #33 of 52 Archive leaderboard report
Atari Games Atari 2600 Pooyan Advantage Learning Score 4801.27 #2 of 3 Archive leaderboard report
Atari Games Atari 2600 Private Eye Advantage Learning Score 5276.16 #14 of 52 Archive leaderboard report
Atari Games Atari 2600 Q*Bert Advantage Learning Score 14368.03 #31 of 57 Archive leaderboard report
Atari Games Atari 2600 River Raid Advantage Learning Score 10585.12 #28 of 41 Archive leaderboard report
Atari Games Atari 2600 Road Runner Advantage Learning Score 52351.23 #24 of 44 Archive leaderboard report
Atari Games Atari 2600 Robotank Advantage Learning Score 69.31 #11 of 42 Archive leaderboard report
Atari Games Atari 2600 Seaquest Persistent AL Score 13230.74 #20 of 57 Archive leaderboard report
Atari Games Atari 2600 Seaquest Advantage Learning Score 8670.5 #24 of 57 Archive leaderboard report
Atari Games Atari 2600 Skiing Advantage Learning Score -13264.51 #12 of 23 Archive leaderboard report
Atari Games Atari 2600 Solaris Advantage Learning Score 4785.16 #14 of 23 Archive leaderboard report
Atari Games Atari 2600 Space Invaders Advantage Learning Score 3460.79 #25 of 55 Archive leaderboard report
Atari Games Atari 2600 Space Invaders Persistent AL Score 3277.59 #26 of 55 Archive leaderboard report
Atari Games Atari 2600 Star Gunner Advantage Learning Score 61353.59 #26 of 43 Archive leaderboard report
Atari Games Atari 2600 Surround Persistent AL Score 0.72 #13 of 15 Archive leaderboard report
Atari Games Atari 2600 Tennis Advantage Learning Score 0 #27 of 43 Archive leaderboard report
Atari Games Atari 2600 Time Pilot Advantage Learning Score 8969.12 #26 of 44 Archive leaderboard report
Atari Games Atari 2600 Tutankham Advantage Learning Score 245.22 #18 of 44 Archive leaderboard report
Atari Games Atari 2600 Up and Down Advantage Learning Score 13909.74 #35 of 44 Archive leaderboard report
Atari Games Atari 2600 Venture Advantage Learning Score 198.69 #29 of 55 Archive leaderboard report
Atari Games Atari 2600 Video Pinball Advantage Learning Score 543504 #15 of 42 Archive leaderboard report
Atari Games Atari 2600 Wizard of Wor Advantage Learning Score 9541.14 #20 of 41 Archive leaderboard report
Atari Games Atari 2600 Yars Revenge Advantage Learning Score 24240.03 #17 of 17 Archive leaderboard report
Atari Games Atari 2600 Zaxxon Advantage Learning Score 9129.61 #31 of 41 Archive leaderboard report

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