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Meta-learning how to Share Credit among Macro-Actions
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Proposes MASP, a regularizer that pushes Q-values of similar macro-actions toward each other via a similarity matrix meta-learned jointly with the policy, improving Rainbow-DQN with macro-actions on Atari and Street Fighter II.
Problem
Adding macro-actions to the action space can hurt exploration because the branching factor grows, and each macro-action is treated as independent and atomic in standard value-based RL.
Approach
A soft penalty ||Q - ΣQ||² that ties Q-values of similar (macro-)actions together, with the similarity matrix Σ meta-learned via meta-gradients jointly with the Q-network, so credit is shared among related macro-actions and the effective action dimension is reduced.
Key results
- On Atari, +MASP reaches Breakout 884.4 vs 379.5 for Rainbow-DQN and Seaquest 23,768.8 vs 19,176.0, with HN ≥100 in many games.
- Rainbow with naive macro-actions degrades as the macro set grows (e.g., Breakout 13.2 at k=1024), while MASP stays at 379.5 at k=1024.
- On StreetFighter II Macro-Actions II, MASP reaches 593,784 vs 537,388.8 for Rainbow-DQN and 565,319.2 for +Macro-Actions.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add macro-actions without MASP | Rainbow-DQN · Breakout | score: 379.5 ± 25.1 -> 252.9 ± 22.2 | Hurt |
| Add macro-actions and meta-learned MASP | Rainbow-DQN · Breakout | score: 379.5 ± 25.1 -> 884.4 ± 74.0 | Helped |
| Add macro-actions and meta-learned MASP | Rainbow-DQN · Frostbite | score: 4,141.1 ± 175.4 -> 5,566.7 ± 317.3 | Helped |
| Add macro-actions and similarity penalty | Rainbow-DQN · Macro-Actions I | score: 187,556 ± 3713.3 -> 236,943 ± 13676.0 | Helped |
| Add macro-actions and similarity penalty | Rainbow-DQN · Macro-Actions II | score: 537,388.8 ± 23829.9 -> 593,784 ± 18262.9 | Helped |
| Add macro-actions and similarity penalty | Rainbow-DQN · Door Key | success rate: 0.83 -> 1 | Helped |
| Increase macro-action count from 64 to 1024 without MASP (ablation) | Rainbow-DQN + Macro-Actions · Breakout | score: 248.1 ± 13.9 -> 13.2 ± 0.5 | Hurt |
| Use MASP with 1024 macro-actions instead of independent macro-actions (ablation) | Rainbow-DQN · Breakout | score: 13.2 ± 0.5 -> 379.5 ± 30.1 | Helped |
| Replace macro-actions with random sequences at P(replace)=0.75 without MASP (ablation) | Rainbow-DQN + Macro-Actions · Breakout | score: 252.9 ± 22.2 -> 76.4 ± 4.8 | Hurt |
| Replace macro-actions with random sequences at P(replace)=0.75 while using MASP (ablation) | Rainbow-DQN + MASP · Breakout | score: 884.4 ± 74.0 -> 503.7 ± 39.6 | Hurt |
| Transfer the learned similarity matrix from a different game | Rainbow-DQN + MASP · Breakout | score: 884.4 ± 74.0; 613.2 ± 57.1; 884.4 ± 74.0; 815.3 ± 66.2 | Mixed |
Surprising findings
- Naively adding macro-actions to Rainbow-DQN lowers performance on most Atari games relative to the baseline.
- Transferring a frozen Σ from another game (e.g., Breakout Σ to Space Invaders) can match or exceed in-domain performance in some cases.
Limitations
- Computational cost of the similarity matrix grows quadratically with the action space; overhead about 20% wallclock.
- Benefit depends on the quality of macro-action extraction, which uses a frequency heuristic on human trajectories.
- Σ is state-independent and its interpretability and transfer properties are not fully understood.
Experimental setup
Datasets: Atari Grand Challenge Dataset Arcade Learning Environment Gym Retro StreetFighter II MiniGrid
Benchmarks: Atari 2600 (57 games) StreetFighter II MiniGrid DoorKey, FourRooms, LockedRoom, ObstructedMaze-Full
Metrics: game score human-normalized score success rate
Baselines: Rainbow-DQN Rainbow-DQN + Macro-Actions
Builds on: Rainbow DQN DQN meta-gradient reinforcement learning universal value function approximators
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