# Directly Forecasting Belief for Reinforcement Learning with Delays

arXiv: https://arxiv.org/abs/2505.00546 · HTML: https://mlsanity.com/paper/2505.00546/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Deep RL algorithms and representations, one of 15 directions in Deep reinforcement learning methods.
- First posted on arXiv 1 May 2025.

## Placed in

- Deep reinforcement learning methods / [Deep RL algorithms and representations](https://mlsanity.com/deeprl/deep-rl-algorithms-and-representations/)

## Built on by (most cited first, 4 of 4)

- [Belief-Based Offline Reinforcement Learning for Delay-Robust Policy Optimization](https://mlsanity.com/paper/2506.00131/) (2025)
- [Reinforcement Learning for Control Systems with Time Delays: A Comprehensive Survey](https://mlsanity.com/paper/2602.00399/) (2026)
- [State-Action Inpainting Diffuser for Continuous Control with Delay](https://mlsanity.com/paper/2603.01553/) (2026)
- [Minimax Optimal Strategy for Delayed Observations in Online Reinforcement Learning](https://mlsanity.com/paper/2603.03480/) (2026)

## Abstract (arXiv)

Reinforcement learning (RL) with delays is challenging as sensory perceptions lag behind the actual events: the RL agent needs to estimate the real state of its environment based on past observations. State-of-the-art (SOTA) methods typically employ recursive, step-by-step forecasting of states. This can cause the accumulation of compounding errors. To tackle this problem, our novel belief estimation method, named Directly Forecasting Belief Transformer (DFBT), directly forecasts states from observations without incrementally estimating intermediate states step-by-step. We theoretically demonstrate that DFBT greatly reduces compounding errors of existing recursively forecasting methods, yielding stronger performance guarantees. In experiments with D4RL offline datasets, DFBT reduces compounding errors with remarkable prediction accuracy. DFBT's capability to forecast state sequences also facilitates multi-step bootstrapping, thus greatly improving learning efficiency. On the MuJoCo benchmark, our DFBT-based method substantially outperforms SOTA baselines. Code is available at https://github.com/QingyuanWuNothing/DFBT.