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Directly Forecasting Belief for Reinforcement Learning with Delays
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Proposes DFBT, a transformer that directly forecasts delayed states from augmented observations instead of recursive step-by-step prediction, and DFBT-SAC, which adds multi-step bootstrapping on those forecasts to improve delayed RL on MuJoCo.
Problem
Reinforcement learning with observation delays, where the agent must estimate the current true state from lagged observations; recursive belief forecasting accumulates compounding errors that grow with delay length.
Approach
Reformulate belief estimation as sequence modeling: a transformer takes the delayed state and the interleaved action/reward tokens and predicts all Δ intermediate states in one pass, avoiding recursive error accumulation, and then uses these predicted states for N-step SAC bootstrapping.
Key results
- On Walker2d-v2 with U(1,128) stochastic delays, DFBT-SAC reaches 0.30 normalized return vs. 0.10 for the best belief baseline (DATS), and on Hopper-v2 with U(1,8) it reaches 0.86.
- DFBT-SAC achieves 0.42 on HalfCheetah-v2 with 32 deterministic delays, the best among belief-based methods, and 0.20 on Hopper-v2 with 128 delays.
- DFBT inference time stays around 4 ms across delays 8 to 128 on HalfCheetah-v2, while DATS and D-Dreamer grow to about 15 ms and 27 ms at 128 delays.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| replace recursive belief forecasting with direct DFBT forecasting | belief-based delayed RL · D4RL mixed dataset, increasing delays | belief prediction error (L1) | Helped |
| use DFBT-SAC instead of the strongest baseline | delayed RL · MuJoCo, deterministic delays 32 and 128 | normalized return | Mixed |
| use DFBT-SAC instead of belief-based baselines | delayed RL · MuJoCo, stochastic delays U(1,8), U(1,32), and U(1,128) | normalized return: 144%; 180%; 100% | Helped |
| add multi-step bootstrapping instead of single-step bootstrapping (ablation) | DFBT-SAC · MuJoCo, deterministic and stochastic delays | normalized return | Helped |
| use 8 rather than 1 bootstrapping step (ablation) | DFBT-SAC · Walker2d-v2, deterministic delay 8 | normalized return: 0.86_{\pm 0.07} -> 1.11_{\pm 0.10} | Helped |
| train the belief offline rather than online (ablation) | DFBT-SAC · HalfCheetah-v2, deterministic delay 32 | normalized return: 0.11\pm 0.39 -> 0.42\pm 0.12 | Helped |
| fine-tune the offline-trained belief during RL (ablation) | DFBT-SAC · Hopper-v2 and Walker2d-v2, deterministic delay 32 | normalized return: 0.68\pm 0.20 -> 0.84\pm 0.04; 0.64\pm 0.10 -> 0.96\pm 0.32 | Helped |
| use direct forecasting rather than recursive forecasting | belief estimation · HalfCheetah-v2, inference delay 128 | inference speed: 14.97\pm 0.22; 26.51\pm 0.19 -> 4.15\pm 0.05 | Helped |
Surprising findings
- Augmentation-based methods (BPQL, ADRL) remain competitive or better than DFBT-SAC at short delays (8), and in several cases (e.g., Walker2d 8 deterministic delays) BPQL/ADRL score above DFBT-SAC.
- Online learning of the belief from scratch was unstable, so the authors train the belief offline and separate it from the RL loop.
Limitations
- Belief is learned offline from a fixed dataset, so its quality depends on dataset quality and quantity; online belief learning was unstable.
- No theoretical sample complexity analysis of directly forecasting belief.
- Augmentation-based baselines outperform DFBT-SAC at short delays.
Experimental setup
Datasets: D4RL MuJoCo
Benchmarks: MuJoCo HalfCheetah-v2 MuJoCo Hopper-v2 MuJoCo Walker2d-v2 D4RL MuJoCo Pusher-v2 MuJoCo Reacher-v2 MuJoCo Swimmer-v2
Metrics: normalized return L1 belief error inference speed (ms)
Baselines: A-SAC BPQL ADRL DATS D-Dreamer D-SAC
Builds on: Soft Actor-Critic augmentation-based delayed RL belief-based delayed RL multi-step learning CORL CleanRL
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