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Initialize policy network πθ, critic networks Q𝜙1 and Q, and target networks Tθ, Q1 and Q2 for each iteration do
Sample transition mini-batch B = {(st, at,rt, St+1)} ~ D. # Q-value function learning
Sample at+1 ~ πθ(at+1|St+1) by Equation (1).
Update Qφ1 and QΦ2 by Equation (4). (max Q backup by Kumar et al. (202O) could be added)
#Policy learning Sample a𝑙 ~ πθ(at |St) by Equation (1).
Update policy by minimizing Equation (3).
# Update target networks
0'=p0'+(1-p)0,Φ²=pΦ+(1-p)Φifori={1,2}. end for
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Gym TasksBCAWACDiffuserMoRelOnestep RLTD3+BCDTCQLIQLDiffusion-QL
halfcheetah-medium-v242.643.544.242.148.448.342.644.047.451.1 ± 0.5
hopper-medium-v252.957.058.595.459.659.367.658.566.390.5 ±4.6
walker2d-medium-v275.372.479.777.881.883.774.072.578.387.0±0.9
halfcheetah-medium-replay-v236.640.542.240.238.144.636.645.544.247.8 ± 0.3
hopper-medium-replay-v218.137.296.893.697.560.982.795.094.7101.3 ± 0.6
walker2d-medium-replay-v226.027.061.249.849.581.866.677.273.995.5 ± 1.5
halfcheetah-medium-expert-v255.242.879.853.393.490.786.891.686.796.8 ± 0.3
hopper-medium-expert-v252.555.8107.2108.7103.398.0107.6105.491.5111.1 ± 1.3
walker2d-medium-expert-v2107.574.5108.495.6113.0110.1108.1108.8109.6110.1 ± 0.3
Average51.950.175.372.976.175.374.777.677.088.0
AntMaze TasksBCAWACBCQBEAROnestep RLTD3+BCDTCQLIQLDiffusion-QL
antmaze-umaze-v054.656.778.973.064.378.659.274.087.593.4±3.4
antmaze-umaze-diverse-v045.649.355.061.060.771.453.084.062.266.2± 8.6
antmaze-medium-play-v00.00.00.00.00.310.60.061.271.276.6 ± 10.8
antmaze-medium-diverse-v00.00.70.08.00.03.00.053.770.078.6 ± 10.3
antmaze-large-play-v00.00.06.70.00.00.20.015.839.646.4 ± 8.3
antmaze-large-diverse-v00.01.02.20.00.00.00.014.947.556.6± 7.6
Average16.718.023.823.720.927.318.750.663.069.6
Adroit TasksBCSACBCQBEARBRAC-pBRAC-vREMCQLIQLDiffusion-QL
pen-human-v125.84.368.9-1.08.10.65.435.271.572.8± 9.6
pen-cloned-v138.3-0.844.026.51.6-2.5-1.027.237.357.3 ± 11.9
Average32.11.856.512.84.9-1.02.231.254.465.1
Kitchen TasksBCSACBCQBEARBRAC-pBRAC-vAWRCQLIQLDiffusion-QL
kitchen-complete-v033.815.08.10.00.00.00.043.862.584.0 ± 7.4
kitchen-partial-vo33.80.018.913.10.00.015.449.846.360.5 ± 6.9
kitchen-mixed-v047.52.58.147.20.00.010.651.051.062.6 ± 5.1
Average38.45.811.720.10.00.08.748.253.369.0
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Gym TasksBC-CVAEBC-DiffusionBCQ-CVAEBCQ-DiffusionCVAE-QLDiffusion-QL
halfcheetah-medium-expert-v267.3± 7.476.6± 7.096.1 ± 0.594.6±1.070.3± 5.597.2 ± 0.4
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walker2d-medium-expert-v2102.5 ± 4.4103.1 ± 4.4110.7 ± 0.2114.0 ± 0.550.5 ±38.2111.2 ± 0.9
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halfcheetah-medium-v23×10-41.0False
hopper-medium-v23×10-41.0False
walker2d-medium-v23×10-41.0False
halfcheetah-medium-replay-v23×10-41.0False
hopper-medium-replay-v23×10-41.0False
walker2d-medium-replay-v23×10-41.0False
halfcheetah-medium-expert-v23×10-41.0False
hopper-medium-expert-v23×10-41.0False
walker2d-medium-expert-v23×10-41.0False
antmaze-umaze-vo3×10-40.5False
antmaze-umaze-diverse-v03×10-42.0True
antmaze-medium-play-v01×10-32.0True
antmaze-medium-diverse-vO3×10-43.0True
antmaze-large-play-vo3×10-44.5True
antmaze-large-diverse-vO3×10-43.5True
pen-human-v13×10-50.15False
pen-cloned-v13×10-50.1False
kitchen-complete-v03×10-40.005False
kitchen-partial-vo3×10-40.005False
kitchen-mixed-v03×10-40.005False
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Gym TasksDiffusion-QL (Offline)Diffusion-QL (Online)
halfcheetah-medium-v251.1 ± 0.551.5 ± 0.3
hopper-medium-v290.5 ± 4.696.6 ± 3.4
walker2d-medium-v287.0 ± 0.987.3 ± 0.5
halfcheetah-medium-replay-v247.8 ± 0.348.3 ± 0.2
hopper-medium-replay-v2101.3 ± 0.6102.0 ± 0.4
walker2d-medium-replay-v295.5 ± 1.598.0 ± 0.5
halfcheetah-medium-expert-v296.8 ± 0.397.2 ± 0.4
hopper-medium-expert-v2111.1 ± 1.3112.3 ± 0.8
walker2d-medium-expert-v2110.1 ± 0.3111.2 ± 0.9
Average88.089.3
AntMaze TasksDiffusion-QL (Offline)Diffusion-QL (Online)
antmaze-umaze-vo93.4 ± 3.496.0 ± 3.3
antmaze-umaze-diverse-v066.2 ± 8.684.0 ± 10.1
antmaze-medium-play-v076.6 ± 10.879.8 ± 8.7
antmaze-medium-diverse-v078.6 ± 10.382.0 ± 9.5
antmaze-large-play-v046.4 ± 8.349.0 ± 9.4
antmaze-large-diverse-v056.6 ± 7.661.7 ± 8.2
Average69.675.4
Adroit TasksDiffusion-QL (Offline)Diffusion-QL (Online)
pen-human-v172.8 ± 9.675.7± 9.0
pen-cloned-v157.3 ± 11.960.8 ± 11.8
Average65.168.3
Kitchen TasksDiffusion-QL (Offline)Diffusion-QL (Online)
kitchen-complete-v084.0 ± 7.484.5 ± 6.1
kitchen-partial-v060.5 ± 6.963.7 ± 5.2
kitchen-mixed-v062.6 ± 5.166.6 ± 3.3
Average69.071.6
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hopper-medium-expert-v298.040.0111.1
walker2d-medium-expert-v2110.166.5110.1
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