TASK	DATASET	MODEL	METRIC NAME	METRIC VALUE	GLOBAL RANK
Atari Games	Atari 2600 Alien	Persistent AL	Score	5699.81	# 15
Atari Games	Atari 2600 Alien	Advantage Learning	Score	4990.91	# 16
Atari Games	Atari 2600 Amidar	Advantage Learning	Score	1557.43	# 15
Atari Games	Atari 2600 Amidar	Persistent AL	Score	1451.65	# 17
Atari Games	Atari 2600 Assault	Persistent AL	Score	3304.33	# 34
Atari Games	Atari 2600 Assault	Advantage Learning	Score	3661.51	# 31
Atari Games	Atari 2600 Asterix	Persistent AL	Score	19564.9	# 26
Atari Games	Atari 2600 Asterix	Advantage Learning	Score	12852.08	# 34
Atari Games	Atari 2600 Asteroids	Advantage Learning	Score	1924.42	# 26
Atari Games	Atari 2600 Asteroids	Persistent AL	Score	1673.52	# 28
Atari Games	Atari 2600 Atlantis	Persistent AL	Score	1465250	# 8
Atari Games	Atari 2600 Atlantis	Advantage Learning	Score	553591.67	# 23
Atari Games	Atari 2600 Bank Heist	Persistent AL	Score	874.99	# 30
Atari Games	Atari 2600 Bank Heist	Advantage Learning	Score	633.63	# 31
Atari Games	Atari 2600 Battle Zone	Persistent AL	Score	34583.07	# 18
Atari Games	Atari 2600 Battle Zone	Advantage Learning	Score	28789.29	# 25
Atari Games	Atari 2600 Beam Rider	Persistent AL	Score	13145.34	# 27
Atari Games	Atari 2600 Beam Rider	Advantage Learning	Score	10054.58	# 30
Atari Games	Atari 2600 Berzerk	Persistent AL	Score	1328.25	# 20
Atari Games	Atari 2600 Berzerk	Advantage Learning	Score	747.26	# 32
Atari Games	Atari 2600 Bowling	Persistent AL	Score	71.59	# 17
Atari Games	Atari 2600 Bowling	Advantage Learning	Score	57.41	# 24
Atari Games	Atari 2600 Boxing	Persistent AL	Score	94.3	# 23
Atari Games	Atari 2600 Boxing	Advantage Learning	Score	93.94	# 24
Atari Games	Atari 2600 Breakout	Advantage Learning	Score	425.32	# 23
Atari Games	Atari 2600 Breakout	Persistent AL	Score	431.89	# 22
Atari Games	Atari 2600 Centipede	Persistent AL	Score	4539.55	# 33
Atari Games	Atari 2600 Centipede	Advantage Learning	Score	4225.18	# 35
Atari Games	Atari 2600 Chopper Command	Persistent AL	Score	5734.93	# 28
Atari Games	Atari 2600 Chopper Command	Advantage Learning	Score	5431.36	# 29
Atari Games	Atari 2600 Crazy Climber	Advantage Learning	Score	123410.71	# 27
Atari Games	Atari 2600 Crazy Climber	Persistent AL	Score	130002.71	# 23
Atari Games	Atari 2600 Defender	Advantage Learning	Score	30643.59	# 19
Atari Games	Atari 2600 Defender	Persistent AL	Score	32038.93	# 18
Atari Games	Atari 2600 Demon Attack	Advantage Learning	Score	27153.48	# 33
Atari Games	Atari 2600 Demon Attack	Persistent AL	Score	70908.17	# 23
Atari Games	Atari 2600 Double Dunk	Advantage Learning	Score	-0.15	# 25
Atari Games	Atari 2600 Double Dunk	Persistent AL	Score	-2.51	# 25
Atari Games	Atari 2600 Elevator Action	Advantage Learning	Score	27088.89	# 2
Atari Games	Atari 2600 Elevator Action	Persistent AL	Score	29100	# 1
Atari Games	Atari 2600 Enduro	Persistent AL	Score	1343.1	# 23
Atari Games	Atari 2600 Enduro	Advantage Learning	Score	1252.7	# 24
Atari Games	Atari 2600 Fishing Derby	Advantage Learning	Score	21.32	# 25
Atari Games	Atari 2600 Fishing Derby	Persistent AL	Score	28.13	# 22
Atari Games	Atari 2600 Freeway	Advantage Learning	Score	31.72	# 26
Atari Games	Atari 2600 Freeway	Persistent AL	Score	32.3	# 24
Atari Games	Atari 2600 Frostbite	Advantage Learning	Score	2305.82	# 29
Atari Games	Atari 2600 Frostbite	Persistent AL	Score	3248.96	# 24
Atari Games	Atari 2600 Gopher	Persistent AL	Score	10611.81	# 28
Atari Games	Atari 2600 Gopher	Advantage Learning	Score	11912.68	# 27
Atari Games	Atari 2600 Gravitar	Advantage Learning	Score	417.65	# 32
Atari Games	Atari 2600 Gravitar	Persistent AL	Score	446.92	# 29
Atari Games	Atari 2600 HERO	Advantage Learning	Score	24788.86	# 18
Atari Games	Atari 2600 HERO	Persistent AL	Score	24175.79	# 19
Atari Games	Atari 2600 Ice Hockey	Persistent AL	Score	-0.25	# 19
Atari Games	Atari 2600 Ice Hockey	Advantage Learning	Score	-1.24	# 19
Atari Games	Atari 2600 James Bond	Advantage Learning	Score	848.46	# 22
Atari Games	Atari 2600 James Bond	Persistent AL	Score	772.09	# 25
Atari Games	Atari 2600 Kangaroo	Persistent AL	Score	11478.46	# 19
Atari Games	Atari 2600 Kangaroo	Advantage Learning	Score	10809.16	# 22
Atari Games	Atari 2600 Krull	Persistent AL	Score	8689.81	# 22
Atari Games	Atari 2600 Krull	Advantage Learning	Score	9548.92	# 20
Atari Games	Atari 2600 Kung-Fu Master	Persistent AL	Score	34650.91	# 23
Atari Games	Atari 2600 Kung-Fu Master	Advantage Learning	Score	32182.99	# 28
Atari Games	Atari 2600 Montezuma's Revenge	Persistent AL	Score	1.72	# 37
Atari Games	Atari 2600 Montezuma's Revenge	Advantage Learning	Score	0.42	# 38
Atari Games	Atari 2600 Ms. Pacman	Persistent AL	Score	3917.55	# 22
Atari Games	Atari 2600 Ms. Pacman	Advantage Learning	Score	4065.8	# 20
Atari Games	Atari 2600 Name This Game	Persistent AL	Score	10431.33	# 29
Atari Games	Atari 2600 Name This Game	Advantage Learning	Score	11025.26	# 25
Atari Games	Atari 2600 Phoenix	Persistent AL	Score	14495.56	# 16
Atari Games	Atari 2600 Phoenix	Advantage Learning	Score	22038.27	# 14
Atari Games	Atari 2600 Pitfall!	Advantage Learning	Score	0	# 4
Atari Games	Atari 2600 Pong	Persistent AL	Score	19.76	# 31
Atari Games	Atari 2600 Pong	Advantage Learning	Score	19.66	# 32
Atari Games	Atari 2600 Pooyan	Advantage Learning	Score	4801.27	# 2
Atari Games	Atari 2600 Private Eye	Advantage Learning	Score	5276.16	# 12
Atari Games	Atari 2600 Q*Bert	Advantage Learning	Score	14368.03	# 29
Atari Games	Atari 2600 River Raid	Advantage Learning	Score	10585.12	# 26
Atari Games	Atari 2600 Road Runner	Advantage Learning	Score	52351.23	# 22
Atari Games	Atari 2600 Robotank	Advantage Learning	Score	69.31	# 11
Atari Games	Atari 2600 Seaquest	Persistent AL	Score	13230.74	# 19
Atari Games	Atari 2600 Seaquest	Advantage Learning	Score	8670.5	# 23
Atari Games	Atari 2600 Skiing	Advantage Learning	Score	-13264.51	# 3
Atari Games	Atari 2600 Solaris	Advantage Learning	Score	4785.16	# 11
Atari Games	Atari 2600 Space Invaders	Advantage Learning	Score	3460.79	# 23
Atari Games	Atari 2600 Space Invaders	Persistent AL	Score	3277.59	# 24
Atari Games	Atari 2600 Star Gunner	Advantage Learning	Score	61353.59	# 24
Atari Games	Atari 2600 Surround	Persistent AL	Score	0.72	# 11
Atari Games	Atari 2600 Tennis	Advantage Learning	Score	0	# 19
Atari Games	Atari 2600 Time Pilot	Advantage Learning	Score	8969.12	# 24
Atari Games	Atari 2600 Tutankham	Advantage Learning	Score	245.22	# 17
Atari Games	Atari 2600 Up and Down	Advantage Learning	Score	13909.74	# 33
Atari Games	Atari 2600 Venture	Advantage Learning	Score	198.69	# 25
Atari Games	Atari 2600 Video Pinball	Advantage Learning	Score	543504	# 14
Atari Games	Atari 2600 Wizard of Wor	Advantage Learning	Score	9541.14	# 18
Atari Games	Atari 2600 Yars Revenge	Advantage Learning	Score	24240.03	# 15
Atari Games	Atari 2600 Zaxxon	Advantage Learning	Score	9129.61	# 29

Badge	Markdown
	`[![PWC](https://img.shields.io/endpoint.svg?url=https://paperswithcode.com/badge/increasing-the-action-gap-new-operators-for/atari-games-on-atari-2600-elevator-action)](https://paperswithcode.com/sota/atari-games-on-atari-2600-elevator-action?p=increasing-the-action-gap-new-operators-for)`
	`[![PWC](https://img.shields.io/endpoint.svg?url=https://paperswithcode.com/badge/increasing-the-action-gap-new-operators-for/atari-games-on-atari-2600-pooyan)](https://paperswithcode.com/sota/atari-games-on-atari-2600-pooyan?p=increasing-the-action-gap-new-operators-for)`
	`[![PWC](https://img.shields.io/endpoint.svg?url=https://paperswithcode.com/badge/increasing-the-action-gap-new-operators-for/atari-games-on-atari-2600-skiing)](https://paperswithcode.com/sota/atari-games-on-atari-2600-skiing?p=increasing-the-action-gap-new-operators-for)`
	`[![PWC](https://img.shields.io/endpoint.svg?url=https://paperswithcode.com/badge/increasing-the-action-gap-new-operators-for/atari-games-on-atari-2600-pitfall)](https://paperswithcode.com/sota/atari-games-on-atari-2600-pitfall?p=increasing-the-action-gap-new-operators-for)`
	`[![PWC](https://img.shields.io/endpoint.svg?url=https://paperswithcode.com/badge/increasing-the-action-gap-new-operators-for/atari-games-on-atari-2600-atlantis)](https://paperswithcode.com/sota/atari-games-on-atari-2600-atlantis?p=increasing-the-action-gap-new-operators-for)`
	`[![PWC](https://img.shields.io/endpoint.svg?url=https://paperswithcode.com/badge/increasing-the-action-gap-new-operators-for/atari-games-on-atari-2600-robotank)](https://paperswithcode.com/sota/atari-games-on-atari-2600-robotank?p=increasing-the-action-gap-new-operators-for)`
	`[![PWC](https://img.shields.io/endpoint.svg?url=https://paperswithcode.com/badge/increasing-the-action-gap-new-operators-for/atari-games-on-atari-2600-solaris)](https://paperswithcode.com/sota/atari-games-on-atari-2600-solaris?p=increasing-the-action-gap-new-operators-for)`
	`[![PWC](https://img.shields.io/endpoint.svg?url=https://paperswithcode.com/badge/increasing-the-action-gap-new-operators-for/atari-games-on-atari-2600-surround)](https://paperswithcode.com/sota/atari-games-on-atari-2600-surround?p=increasing-the-action-gap-new-operators-for)`
	`[![PWC](https://img.shields.io/endpoint.svg?url=https://paperswithcode.com/badge/increasing-the-action-gap-new-operators-for/atari-games-on-atari-2600-private-eye)](https://paperswithcode.com/sota/atari-games-on-atari-2600-private-eye?p=increasing-the-action-gap-new-operators-for)`
	`[![PWC](https://img.shields.io/endpoint.svg?url=https://paperswithcode.com/badge/increasing-the-action-gap-new-operators-for/atari-games-on-atari-2600-phoenix)](https://paperswithcode.com/sota/atari-games-on-atari-2600-phoenix?p=increasing-the-action-gap-new-operators-for)`
	`[![PWC](https://img.shields.io/endpoint.svg?url=https://paperswithcode.com/badge/increasing-the-action-gap-new-operators-for/atari-games-on-atari-2600-video-pinball)](https://paperswithcode.com/sota/atari-games-on-atari-2600-video-pinball?p=increasing-the-action-gap-new-operators-for)`
	`[![PWC](https://img.shields.io/endpoint.svg?url=https://paperswithcode.com/badge/increasing-the-action-gap-new-operators-for/atari-games-on-atari-2600-alien)](https://paperswithcode.com/sota/atari-games-on-atari-2600-alien?p=increasing-the-action-gap-new-operators-for)`
	`[![PWC](https://img.shields.io/endpoint.svg?url=https://paperswithcode.com/badge/increasing-the-action-gap-new-operators-for/atari-games-on-atari-2600-amidar)](https://paperswithcode.com/sota/atari-games-on-atari-2600-amidar?p=increasing-the-action-gap-new-operators-for)`
	`[![PWC](https://img.shields.io/endpoint.svg?url=https://paperswithcode.com/badge/increasing-the-action-gap-new-operators-for/atari-games-on-atari-2600-yars-revenge)](https://paperswithcode.com/sota/atari-games-on-atari-2600-yars-revenge?p=increasing-the-action-gap-new-operators-for)`
	`[![PWC](https://img.shields.io/endpoint.svg?url=https://paperswithcode.com/badge/increasing-the-action-gap-new-operators-for/atari-games-on-atari-2600-bowling)](https://paperswithcode.com/sota/atari-games-on-atari-2600-bowling?p=increasing-the-action-gap-new-operators-for)`
	`[![PWC](https://img.shields.io/endpoint.svg?url=https://paperswithcode.com/badge/increasing-the-action-gap-new-operators-for/atari-games-on-atari-2600-tutankham)](https://paperswithcode.com/sota/atari-games-on-atari-2600-tutankham?p=increasing-the-action-gap-new-operators-for)`
	`[![PWC](https://img.shields.io/endpoint.svg?url=https://paperswithcode.com/badge/increasing-the-action-gap-new-operators-for/atari-games-on-atari-2600-battle-zone)](https://paperswithcode.com/sota/atari-games-on-atari-2600-battle-zone?p=increasing-the-action-gap-new-operators-for)`
	`[![PWC](https://img.shields.io/endpoint.svg?url=https://paperswithcode.com/badge/increasing-the-action-gap-new-operators-for/atari-games-on-atari-2600-defender)](https://paperswithcode.com/sota/atari-games-on-atari-2600-defender?p=increasing-the-action-gap-new-operators-for)`
	`[![PWC](https://img.shields.io/endpoint.svg?url=https://paperswithcode.com/badge/increasing-the-action-gap-new-operators-for/atari-games-on-atari-2600-hero)](https://paperswithcode.com/sota/atari-games-on-atari-2600-hero?p=increasing-the-action-gap-new-operators-for)`
	`[![PWC](https://img.shields.io/endpoint.svg?url=https://paperswithcode.com/badge/increasing-the-action-gap-new-operators-for/atari-games-on-atari-2600-wizard-of-wor)](https://paperswithcode.com/sota/atari-games-on-atari-2600-wizard-of-wor?p=increasing-the-action-gap-new-operators-for)`
	`[![PWC](https://img.shields.io/endpoint.svg?url=https://paperswithcode.com/badge/increasing-the-action-gap-new-operators-for/atari-games-on-atari-2600-ice-hockey)](https://paperswithcode.com/sota/atari-games-on-atari-2600-ice-hockey?p=increasing-the-action-gap-new-operators-for)`
	`[![PWC](https://img.shields.io/endpoint.svg?url=https://paperswithcode.com/badge/increasing-the-action-gap-new-operators-for/atari-games-on-atari-2600-kangaroo)](https://paperswithcode.com/sota/atari-games-on-atari-2600-kangaroo?p=increasing-the-action-gap-new-operators-for)`
	`[![PWC](https://img.shields.io/endpoint.svg?url=https://paperswithcode.com/badge/increasing-the-action-gap-new-operators-for/atari-games-on-atari-2600-seaquest)](https://paperswithcode.com/sota/atari-games-on-atari-2600-seaquest?p=increasing-the-action-gap-new-operators-for)`
	`[![PWC](https://img.shields.io/endpoint.svg?url=https://paperswithcode.com/badge/increasing-the-action-gap-new-operators-for/atari-games-on-atari-2600-tennis)](https://paperswithcode.com/sota/atari-games-on-atari-2600-tennis?p=increasing-the-action-gap-new-operators-for)`
	`[![PWC](https://img.shields.io/endpoint.svg?url=https://paperswithcode.com/badge/increasing-the-action-gap-new-operators-for/atari-games-on-atari-2600-berzerk)](https://paperswithcode.com/sota/atari-games-on-atari-2600-berzerk?p=increasing-the-action-gap-new-operators-for)`
	`[![PWC](https://img.shields.io/endpoint.svg?url=https://paperswithcode.com/badge/increasing-the-action-gap-new-operators-for/atari-games-on-atari-2600-krull)](https://paperswithcode.com/sota/atari-games-on-atari-2600-krull?p=increasing-the-action-gap-new-operators-for)`
	`[![PWC](https://img.shields.io/endpoint.svg?url=https://paperswithcode.com/badge/increasing-the-action-gap-new-operators-for/atari-games-on-atari-2600-ms-pacman)](https://paperswithcode.com/sota/atari-games-on-atari-2600-ms-pacman?p=increasing-the-action-gap-new-operators-for)`
	`[![PWC](https://img.shields.io/endpoint.svg?url=https://paperswithcode.com/badge/increasing-the-action-gap-new-operators-for/atari-games-on-atari-2600-breakout)](https://paperswithcode.com/sota/atari-games-on-atari-2600-breakout?p=increasing-the-action-gap-new-operators-for)`
	`[![PWC](https://img.shields.io/endpoint.svg?url=https://paperswithcode.com/badge/increasing-the-action-gap-new-operators-for/atari-games-on-atari-2600-fishing-derby)](https://paperswithcode.com/sota/atari-games-on-atari-2600-fishing-derby?p=increasing-the-action-gap-new-operators-for)`
	`[![PWC](https://img.shields.io/endpoint.svg?url=https://paperswithcode.com/badge/increasing-the-action-gap-new-operators-for/atari-games-on-atari-2600-james-bond)](https://paperswithcode.com/sota/atari-games-on-atari-2600-james-bond?p=increasing-the-action-gap-new-operators-for)`
	`[![PWC](https://img.shields.io/endpoint.svg?url=https://paperswithcode.com/badge/increasing-the-action-gap-new-operators-for/atari-games-on-atari-2600-road-runner)](https://paperswithcode.com/sota/atari-games-on-atari-2600-road-runner?p=increasing-the-action-gap-new-operators-for)`
	`[![PWC](https://img.shields.io/endpoint.svg?url=https://paperswithcode.com/badge/increasing-the-action-gap-new-operators-for/atari-games-on-atari-2600-boxing)](https://paperswithcode.com/sota/atari-games-on-atari-2600-boxing?p=increasing-the-action-gap-new-operators-for)`
	`[![PWC](https://img.shields.io/endpoint.svg?url=https://paperswithcode.com/badge/increasing-the-action-gap-new-operators-for/atari-games-on-atari-2600-crazy-climber)](https://paperswithcode.com/sota/atari-games-on-atari-2600-crazy-climber?p=increasing-the-action-gap-new-operators-for)`
	`[![PWC](https://img.shields.io/endpoint.svg?url=https://paperswithcode.com/badge/increasing-the-action-gap-new-operators-for/atari-games-on-atari-2600-demon-attack)](https://paperswithcode.com/sota/atari-games-on-atari-2600-demon-attack?p=increasing-the-action-gap-new-operators-for)`
	`[![PWC](https://img.shields.io/endpoint.svg?url=https://paperswithcode.com/badge/increasing-the-action-gap-new-operators-for/atari-games-on-atari-2600-enduro)](https://paperswithcode.com/sota/atari-games-on-atari-2600-enduro?p=increasing-the-action-gap-new-operators-for)`
	`[![PWC](https://img.shields.io/endpoint.svg?url=https://paperswithcode.com/badge/increasing-the-action-gap-new-operators-for/atari-games-on-atari-2600-kung-fu-master)](https://paperswithcode.com/sota/atari-games-on-atari-2600-kung-fu-master?p=increasing-the-action-gap-new-operators-for)`
	`[![PWC](https://img.shields.io/endpoint.svg?url=https://paperswithcode.com/badge/increasing-the-action-gap-new-operators-for/atari-games-on-atari-2600-space-invaders)](https://paperswithcode.com/sota/atari-games-on-atari-2600-space-invaders?p=increasing-the-action-gap-new-operators-for)`
	`[![PWC](https://img.shields.io/endpoint.svg?url=https://paperswithcode.com/badge/increasing-the-action-gap-new-operators-for/atari-games-on-atari-2600-freeway)](https://paperswithcode.com/sota/atari-games-on-atari-2600-freeway?p=increasing-the-action-gap-new-operators-for)`
	`[![PWC](https://img.shields.io/endpoint.svg?url=https://paperswithcode.com/badge/increasing-the-action-gap-new-operators-for/atari-games-on-atari-2600-frostbite)](https://paperswithcode.com/sota/atari-games-on-atari-2600-frostbite?p=increasing-the-action-gap-new-operators-for)`
	`[![PWC](https://img.shields.io/endpoint.svg?url=https://paperswithcode.com/badge/increasing-the-action-gap-new-operators-for/atari-games-on-atari-2600-star-gunner)](https://paperswithcode.com/sota/atari-games-on-atari-2600-star-gunner?p=increasing-the-action-gap-new-operators-for)`
	`[![PWC](https://img.shields.io/endpoint.svg?url=https://paperswithcode.com/badge/increasing-the-action-gap-new-operators-for/atari-games-on-atari-2600-time-pilot)](https://paperswithcode.com/sota/atari-games-on-atari-2600-time-pilot?p=increasing-the-action-gap-new-operators-for)`
	`[![PWC](https://img.shields.io/endpoint.svg?url=https://paperswithcode.com/badge/increasing-the-action-gap-new-operators-for/atari-games-on-atari-2600-double-dunk)](https://paperswithcode.com/sota/atari-games-on-atari-2600-double-dunk?p=increasing-the-action-gap-new-operators-for)`
	`[![PWC](https://img.shields.io/endpoint.svg?url=https://paperswithcode.com/badge/increasing-the-action-gap-new-operators-for/atari-games-on-atari-2600-name-this-game)](https://paperswithcode.com/sota/atari-games-on-atari-2600-name-this-game?p=increasing-the-action-gap-new-operators-for)`
	`[![PWC](https://img.shields.io/endpoint.svg?url=https://paperswithcode.com/badge/increasing-the-action-gap-new-operators-for/atari-games-on-atari-2600-venture)](https://paperswithcode.com/sota/atari-games-on-atari-2600-venture?p=increasing-the-action-gap-new-operators-for)`
	`[![PWC](https://img.shields.io/endpoint.svg?url=https://paperswithcode.com/badge/increasing-the-action-gap-new-operators-for/atari-games-on-atari-2600-asterix)](https://paperswithcode.com/sota/atari-games-on-atari-2600-asterix?p=increasing-the-action-gap-new-operators-for)`
	`[![PWC](https://img.shields.io/endpoint.svg?url=https://paperswithcode.com/badge/increasing-the-action-gap-new-operators-for/atari-games-on-atari-2600-asteroids)](https://paperswithcode.com/sota/atari-games-on-atari-2600-asteroids?p=increasing-the-action-gap-new-operators-for)`
	`[![PWC](https://img.shields.io/endpoint.svg?url=https://paperswithcode.com/badge/increasing-the-action-gap-new-operators-for/atari-games-on-atari-2600-river-raid)](https://paperswithcode.com/sota/atari-games-on-atari-2600-river-raid?p=increasing-the-action-gap-new-operators-for)`
	`[![PWC](https://img.shields.io/endpoint.svg?url=https://paperswithcode.com/badge/increasing-the-action-gap-new-operators-for/atari-games-on-atari-2600-beam-rider)](https://paperswithcode.com/sota/atari-games-on-atari-2600-beam-rider?p=increasing-the-action-gap-new-operators-for)`
	`[![PWC](https://img.shields.io/endpoint.svg?url=https://paperswithcode.com/badge/increasing-the-action-gap-new-operators-for/atari-games-on-atari-2600-gopher)](https://paperswithcode.com/sota/atari-games-on-atari-2600-gopher?p=increasing-the-action-gap-new-operators-for)`
	`[![PWC](https://img.shields.io/endpoint.svg?url=https://paperswithcode.com/badge/increasing-the-action-gap-new-operators-for/atari-games-on-atari-2600-chopper-command)](https://paperswithcode.com/sota/atari-games-on-atari-2600-chopper-command?p=increasing-the-action-gap-new-operators-for)`
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	`[![PWC](https://img.shields.io/endpoint.svg?url=https://paperswithcode.com/badge/increasing-the-action-gap-new-operators-for/atari-games-on-atari-2600-qbert)](https://paperswithcode.com/sota/atari-games-on-atari-2600-qbert?p=increasing-the-action-gap-new-operators-for)`
	`[![PWC](https://img.shields.io/endpoint.svg?url=https://paperswithcode.com/badge/increasing-the-action-gap-new-operators-for/atari-games-on-atari-2600-zaxxon)](https://paperswithcode.com/sota/atari-games-on-atari-2600-zaxxon?p=increasing-the-action-gap-new-operators-for)`
	`[![PWC](https://img.shields.io/endpoint.svg?url=https://paperswithcode.com/badge/increasing-the-action-gap-new-operators-for/atari-games-on-atari-2600-bank-heist)](https://paperswithcode.com/sota/atari-games-on-atari-2600-bank-heist?p=increasing-the-action-gap-new-operators-for)`
	`[![PWC](https://img.shields.io/endpoint.svg?url=https://paperswithcode.com/badge/increasing-the-action-gap-new-operators-for/atari-games-on-atari-2600-assault)](https://paperswithcode.com/sota/atari-games-on-atari-2600-assault?p=increasing-the-action-gap-new-operators-for)`
	`[![PWC](https://img.shields.io/endpoint.svg?url=https://paperswithcode.com/badge/increasing-the-action-gap-new-operators-for/atari-games-on-atari-2600-pong)](https://paperswithcode.com/sota/atari-games-on-atari-2600-pong?p=increasing-the-action-gap-new-operators-for)`
	`[![PWC](https://img.shields.io/endpoint.svg?url=https://paperswithcode.com/badge/increasing-the-action-gap-new-operators-for/atari-games-on-atari-2600-centipede)](https://paperswithcode.com/sota/atari-games-on-atari-2600-centipede?p=increasing-the-action-gap-new-operators-for)`
	`[![PWC](https://img.shields.io/endpoint.svg?url=https://paperswithcode.com/badge/increasing-the-action-gap-new-operators-for/atari-games-on-atari-2600-up-and-down)](https://paperswithcode.com/sota/atari-games-on-atari-2600-up-and-down?p=increasing-the-action-gap-new-operators-for)`
	`[![PWC](https://img.shields.io/endpoint.svg?url=https://paperswithcode.com/badge/increasing-the-action-gap-new-operators-for/atari-games-on-atari-2600-montezumas-revenge)](https://paperswithcode.com/sota/atari-games-on-atari-2600-montezumas-revenge?p=increasing-the-action-gap-new-operators-for)`

Increasing the Action Gap: New Operators for Reinforcement Learning

15 Dec 2015 · 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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Task	Dataset	Model	Metric Name	Metric Value	Global Rank	Benchmark
Atari Games	Atari 2600 Alien	Persistent AL	Score	5699.81	# 15	Compare
Atari Games	Atari 2600 Alien	Advantage Learning	Score	4990.91	# 16	Compare
Atari Games	Atari 2600 Amidar	Advantage Learning	Score	1557.43	# 15	Compare
Atari Games	Atari 2600 Amidar	Persistent AL	Score	1451.65	# 17	Compare
Atari Games	Atari 2600 Assault	Persistent AL	Score	3304.33	# 34	Compare
Atari Games	Atari 2600 Assault	Advantage Learning	Score	3661.51	# 31	Compare
Atari Games	Atari 2600 Asterix	Persistent AL	Score	19564.9	# 26	Compare
Atari Games	Atari 2600 Asterix	Advantage Learning	Score	12852.08	# 34	Compare
Atari Games	Atari 2600 Asteroids	Advantage Learning	Score	1924.42	# 26	Compare
Atari Games	Atari 2600 Asteroids	Persistent AL	Score	1673.52	# 28	Compare
Atari Games	Atari 2600 Atlantis	Persistent AL	Score	1465250	# 8	Compare
Atari Games	Atari 2600 Atlantis	Advantage Learning	Score	553591.67	# 23	Compare
Atari Games	Atari 2600 Bank Heist	Persistent AL	Score	874.99	# 30	Compare
Atari Games	Atari 2600 Bank Heist	Advantage Learning	Score	633.63	# 31	Compare
Atari Games	Atari 2600 Battle Zone	Persistent AL	Score	34583.07	# 18	Compare
Atari Games	Atari 2600 Battle Zone	Advantage Learning	Score	28789.29	# 25	Compare
Atari Games	Atari 2600 Beam Rider	Persistent AL	Score	13145.34	# 27	Compare
Atari Games	Atari 2600 Beam Rider	Advantage Learning	Score	10054.58	# 30	Compare
Atari Games	Atari 2600 Berzerk	Persistent AL	Score	1328.25	# 20	Compare
Atari Games	Atari 2600 Berzerk	Advantage Learning	Score	747.26	# 32	Compare
Atari Games	Atari 2600 Bowling	Persistent AL	Score	71.59	# 17	Compare
Atari Games	Atari 2600 Bowling	Advantage Learning	Score	57.41	# 24	Compare
Atari Games	Atari 2600 Boxing	Persistent AL	Score	94.3	# 23	Compare
Atari Games	Atari 2600 Boxing	Advantage Learning	Score	93.94	# 24	Compare
Atari Games	Atari 2600 Breakout	Advantage Learning	Score	425.32	# 23	Compare
Atari Games	Atari 2600 Breakout	Persistent AL	Score	431.89	# 22	Compare
Atari Games	Atari 2600 Centipede	Persistent AL	Score	4539.55	# 33	Compare
Atari Games	Atari 2600 Centipede	Advantage Learning	Score	4225.18	# 35	Compare
Atari Games	Atari 2600 Chopper Command	Persistent AL	Score	5734.93	# 28	Compare
Atari Games	Atari 2600 Chopper Command	Advantage Learning	Score	5431.36	# 29	Compare
Atari Games	Atari 2600 Crazy Climber	Advantage Learning	Score	123410.71	# 27	Compare
Atari Games	Atari 2600 Crazy Climber	Persistent AL	Score	130002.71	# 23	Compare
Atari Games	Atari 2600 Defender	Advantage Learning	Score	30643.59	# 19	Compare
Atari Games	Atari 2600 Defender	Persistent AL	Score	32038.93	# 18	Compare
Atari Games	Atari 2600 Demon Attack	Advantage Learning	Score	27153.48	# 33	Compare
Atari Games	Atari 2600 Demon Attack	Persistent AL	Score	70908.17	# 23	Compare
Atari Games	Atari 2600 Double Dunk	Advantage Learning	Score	-0.15	# 25	Compare
Atari Games	Atari 2600 Double Dunk	Persistent AL	Score	-2.51	# 25	Compare
Atari Games	Atari 2600 Elevator Action	Advantage Learning	Score	27088.89	# 2	Compare
Atari Games	Atari 2600 Elevator Action	Persistent AL	Score	29100	# 1	Compare
Atari Games	Atari 2600 Enduro	Persistent AL	Score	1343.1	# 23	Compare
Atari Games	Atari 2600 Enduro	Advantage Learning	Score	1252.7	# 24	Compare
Atari Games	Atari 2600 Fishing Derby	Advantage Learning	Score	21.32	# 25	Compare
Atari Games	Atari 2600 Fishing Derby	Persistent AL	Score	28.13	# 22	Compare
Atari Games	Atari 2600 Freeway	Advantage Learning	Score	31.72	# 26	Compare
Atari Games	Atari 2600 Freeway	Persistent AL	Score	32.3	# 24	Compare
Atari Games	Atari 2600 Frostbite	Advantage Learning	Score	2305.82	# 29	Compare
Atari Games	Atari 2600 Frostbite	Persistent AL	Score	3248.96	# 24	Compare
Atari Games	Atari 2600 Gopher	Persistent AL	Score	10611.81	# 28	Compare
Atari Games	Atari 2600 Gopher	Advantage Learning	Score	11912.68	# 27	Compare
Atari Games	Atari 2600 Gravitar	Advantage Learning	Score	417.65	# 32	Compare
Atari Games	Atari 2600 Gravitar	Persistent AL	Score	446.92	# 29	Compare
Atari Games	Atari 2600 HERO	Advantage Learning	Score	24788.86	# 18	Compare
Atari Games	Atari 2600 HERO	Persistent AL	Score	24175.79	# 19	Compare
Atari Games	Atari 2600 Ice Hockey	Persistent AL	Score	-0.25	# 19	Compare
Atari Games	Atari 2600 Ice Hockey	Advantage Learning	Score	-1.24	# 19	Compare
Atari Games	Atari 2600 James Bond	Advantage Learning	Score	848.46	# 22	Compare
Atari Games	Atari 2600 James Bond	Persistent AL	Score	772.09	# 25	Compare
Atari Games	Atari 2600 Kangaroo	Persistent AL	Score	11478.46	# 19	Compare
Atari Games	Atari 2600 Kangaroo	Advantage Learning	Score	10809.16	# 22	Compare
Atari Games	Atari 2600 Krull	Persistent AL	Score	8689.81	# 22	Compare
Atari Games	Atari 2600 Krull	Advantage Learning	Score	9548.92	# 20	Compare
Atari Games	Atari 2600 Kung-Fu Master	Persistent AL	Score	34650.91	# 23	Compare
Atari Games	Atari 2600 Kung-Fu Master	Advantage Learning	Score	32182.99	# 28	Compare
Atari Games	Atari 2600 Montezuma's Revenge	Persistent AL	Score	1.72	# 37	Compare
Atari Games	Atari 2600 Montezuma's Revenge	Advantage Learning	Score	0.42	# 38	Compare
Atari Games	Atari 2600 Ms. Pacman	Persistent AL	Score	3917.55	# 22	Compare
Atari Games	Atari 2600 Ms. Pacman	Advantage Learning	Score	4065.8	# 20	Compare
Atari Games	Atari 2600 Name This Game	Persistent AL	Score	10431.33	# 29	Compare
Atari Games	Atari 2600 Name This Game	Advantage Learning	Score	11025.26	# 25	Compare
Atari Games	Atari 2600 Phoenix	Persistent AL	Score	14495.56	# 16	Compare
Atari Games	Atari 2600 Phoenix	Advantage Learning	Score	22038.27	# 14	Compare
Atari Games	Atari 2600 Pitfall!	Advantage Learning	Score	0	# 4	Compare
Atari Games	Atari 2600 Pong	Persistent AL	Score	19.76	# 31	Compare
Atari Games	Atari 2600 Pong	Advantage Learning	Score	19.66	# 32	Compare
Atari Games	Atari 2600 Pooyan	Advantage Learning	Score	4801.27	# 2	Compare
Atari Games	Atari 2600 Private Eye	Advantage Learning	Score	5276.16	# 12	Compare
Atari Games	Atari 2600 Q*Bert	Advantage Learning	Score	14368.03	# 29	Compare
Atari Games	Atari 2600 River Raid	Advantage Learning	Score	10585.12	# 26	Compare
Atari Games	Atari 2600 Road Runner	Advantage Learning	Score	52351.23	# 22	Compare
Atari Games	Atari 2600 Robotank	Advantage Learning	Score	69.31	# 11	Compare
Atari Games	Atari 2600 Seaquest	Persistent AL	Score	13230.74	# 19	Compare
Atari Games	Atari 2600 Seaquest	Advantage Learning	Score	8670.5	# 23	Compare
Atari Games	Atari 2600 Skiing	Advantage Learning	Score	-13264.51	# 3	Compare
Atari Games	Atari 2600 Solaris	Advantage Learning	Score	4785.16	# 11	Compare
Atari Games	Atari 2600 Space Invaders	Advantage Learning	Score	3460.79	# 23	Compare
Atari Games	Atari 2600 Space Invaders	Persistent AL	Score	3277.59	# 24	Compare
Atari Games	Atari 2600 Star Gunner	Advantage Learning	Score	61353.59	# 24	Compare
Atari Games	Atari 2600 Surround	Persistent AL	Score	0.72	# 11	Compare
Atari Games	Atari 2600 Tennis	Advantage Learning	Score	0	# 19	Compare
Atari Games	Atari 2600 Time Pilot	Advantage Learning	Score	8969.12	# 24	Compare
Atari Games	Atari 2600 Tutankham	Advantage Learning	Score	245.22	# 17	Compare
Atari Games	Atari 2600 Up and Down	Advantage Learning	Score	13909.74	# 33	Compare
Atari Games	Atari 2600 Venture	Advantage Learning	Score	198.69	# 25	Compare
Atari Games	Atari 2600 Video Pinball	Advantage Learning	Score	543504	# 14	Compare
Atari Games	Atari 2600 Wizard of Wor	Advantage Learning	Score	9541.14	# 18	Compare
Atari Games	Atari 2600 Yars Revenge	Advantage Learning	Score	24240.03	# 15	Compare
Atari Games	Atari 2600 Zaxxon	Advantage Learning	Score	9129.61	# 29	Compare

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