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Adversarially Robust Decision Transformer
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Proposes ARDT, a worst-case-aware Decision Transformer that relabels returns-to-go with in-sample minimax values learned via expectile regression, improving robustness to powerful test-time adversaries in offline adversarial RL.
Problem
Decision Transformer-style RvS methods are non-robust in adversarial offline RL because return-conditioned policies learn from trajectories whose returns reflect weak behavior adversaries, so they fail against stronger test-time adversaries.
Approach
Relabel each trajectory's returns-to-go with an in-sample minimax return estimated by coupled expectile regression (minimum over dataset adversary actions, maximum over protagonist actions), then train a standard Decision Transformer conditioned on these worst-case returns-to-go.
Key results
- On full-coverage single-stage, Gambling, and multi-stage games, ARDT reaches the maximin (Nash) worst-case return when conditioned on large target return, whereas vanilla DT fails.
- On Connect Four with partial coverage, ARDT with mixed near-random/near-optimal data achieves 0.55 average return vs 0.18 for DT against a 30%-optimal adversary.
- On MuJoCo NR-MDP, ARDT attains higher worst-case return than DT and ESPER on Hopper-hr-type settings (e.g., Hopper-lr 477.9 vs 112.1 for DT and 66.8 for ESPER) and is competitive on Halfcheetah.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| minimax (worst-case) return relabeling with expectile regression instead of observed/expected returns | Decision Transformer · Connect Four mixed data, 30% optimal test adversary | average return: 0.18 to 0.55 | Helped |
| minimax return relabeling (ARDT) vs vanilla DT | Decision Transformer · Connect Four mixed data, 70% optimal test adversary | average return: -0.57 to 0.02 | Helped |
| minimax return relabeling (ARDT) vs vanilla DT | Decision Transformer · Connect Four mixed data, 100% optimal test adversary | average return: both -1 | No clear effect |
| minimax return relabeling (ARDT) vs vanilla DT | Decision Transformer · Hopper-lr, NR-MDP worst-case over 8 adversaries | worst-case return: 112.1 to 477.9 | Helped |
| minimax return relabeling (ARDT) vs expected return relabeling (ESPER) | Decision Transformer · Hopper-lr, NR-MDP worst-case over 8 adversaries | worst-case return: 66.8 to 477.9 | Helped |
| minimax return relabeling (ARDT) vs vanilla DT | Decision Transformer · Halfcheetah-lr, NR-MDP worst-case | worst-case return: 1416.0 to 1509.2 | Helped |
| minimax return relabeling (ARDT) vs expected return relabeling (ESPER) | Decision Transformer · Halfcheetah-lr, NR-MDP worst-case | worst-case return: 1691.8 to 1509.2 | Hurt |
| minimax return relabeling (ARDT) vs expected return relabeling (ESPER) | Decision Transformer · Halfcheetah-mr, NR-MDP worst-case | worst-case return: 1725.6 to 1594.6 | Hurt |
| minimax return relabeling (ARDT) vs vanilla DT and ESPER on Walker2D | Decision Transformer · Walker2D NR-MDP worst-case (lr/mr/hr) | worst-case return: ARDT 405.6 vs DT 429.6 (lr); 508.4 vs 391.0 (mr); 492.63 vs 413.22 (hr) | Mixed |
| expectile level lowered from 0.3 toward 0.01 (more minimax-like relabeling) (ablation) | ARDT on single-stage and multi-stage games · Single-stage and Multi-stage games with optimal adversary | worst-case return: qualitative: smaller alpha yields more robustness | Helped |
| expectile level too small (0.01) on Connect Four (ablation) | ARDT on Connect Four · Connect Four vs epsilon-greedy adversary (eps=0.5) | average return: performance rises then drops as alpha decreases; alpha=0.01 overly conservative | Mixed |
| training on sequences without adversarial tokens (vs with adversarial tokens) (ablation) | ARDT on NR-MDP MuJoCo · Hopper-lr worst-case over 8 adversaries | worst-case return: 302.0 to 477.9 | Helped |
Surprising findings
- Vanilla DT conditioned on the largest worst-case return can still fail in the Gambling environment, showing that conditioning on the robust return alone is insufficient without minimax relabeling.
- Overly small expectile level (alpha=0.01) made ARDT too conservative in Connect Four, so performance peaked at intermediate alpha values.
Limitations
- Practical algorithm estimates minimax returns-to-go without accounting for environment stochasticity; the theory assumes deterministic transitions given joint actions.
- Under low data coverage, learning a single worst-case value may be limiting compared to expectation-based methods.
- Performance is sensitive to the expectile level; too small alpha can make the policy overly conservative.
Experimental setup
Datasets: Single-stage Game (enumerated) Gambling (adversarial) Multi-stage Game Connect Four (solver-generated epsilon-greedy data) MuJoCo Noisy Action Robust MDP datasets (Hopper, Walker2D, Halfcheetah)
Benchmarks: Single-stage Game Gambling Multi-stage Game Connect Four MuJoCo NR-MDP (Hopper, Walker2D, Halfcheetah)
Metrics: worst-case return average return return drop
Baselines: Decision Transformer ESPER
Builds on: Decision Transformer ESPER Implicit Q-Learning Hindsight Information Matching Action Robust RL (ARRL)
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