Source-linked AI summary
Time Limits in Reinforcement Learning
Fabio Pardo, Arash Tavakoli, Vitaly Levdik, Petar Kormushev
TL;DR
The paper addresses how reinforcement learning should handle time limits when optimizing either a finite-horizon or an indefinite-horizon objective. It formalizes time-awareness and partial-episode bootstrapping, and reports significant performance and stability improvements across reinforcement learning algorithms and control tasks.
Problem
Time limits can cause state aliasing and invalidate experience replay when agents do not distinguish finite-horizon objectives from training-only episode truncations.
Method
The paper includes remaining time in observations for time-limited tasks and continues bootstrapping across time-limit terminations for time-unlimited tasks.
Results
The proposed treatments significantly improve performance and stability, including outperforming standard PPO on time-unlimited tasks and improving PPO on time-limited tasks.
Takeaways & Limitations
Time limits should be handled according to whether they define the task objective or merely diversify experience during training.
Takeaways & Limitations
Time-awareness may be less consequential when timeouts are rarely experienced, observations correlate with time, repeated states at different remaining times are unlikely, or discounting is sufficiently small.
Abstract
from arXiv · showhide
In reinforcement learning, it is common to let an agent interact for a fixed amount of time with its environment before resetting it and repeating the process in a series of episodes. The task that the agent has to learn can either be to maximize its performance over (i) that fixed period, or (ii) an indefinite period where time limits are only used during training to diversify experience. In this paper, we provide a formal account for how time limits could effectively be handled in each of the two cases and explain why not doing so can cause state aliasing and invalidation of experience replay, leading to suboptimal policies and training instability. In case (i), we argue that the terminations due to time limits are in fact part of the environment, and thus a notion of the remaining time should be included as part of the agent's input to avoid violation of the Markov property. In case (ii), the time limits are not part of the environment and are only used to facilitate learning. We argue that this insight should be incorporated by bootstrapping from the value of the state at the end of each partial episode. For both cases, we illustrate empirically the significance of our considerations in improving the performance and stability of existing reinforcement learning algorithms, showing state-of-the-art results on several control tasks.
1. Introduction
The paper distinguishes time-limited objectives from time-unlimited objectives trained with partial episodes, showing that each requires a different treatment of time-limit terminations. It formalizes time-awareness and partial-episode bootstrapping and reports improved performance and stability for existing reinforcement learning algorithms.
- Time-limited objectives: Time-limited objectives require representing remaining time in the agent’s input because time-limit terminations are part of the environment’s state.Without this information, states with different remaining times can be confused, violating the Markov property.
- Failure modes: Time-unaware agents can learn suboptimal policies and unstable value estimates because states differing only in remaining time appear identical.The paper identifies this as state aliasing and links it to infeasible credit assignment.
- Time-unlimited objectives: Time-unlimited objectives should bootstrap from non-terminal states reached at time limits instead of treating partial-episode endings as environmental terminations.This partial-episode bootstrapping approach supports policies intended to continue beyond training time limits.
- Evaluation: The study evaluates tabular Q-learning and PPO across novel and established benchmark domains using the OpenAI Baselines PPO implementation.The experiments use the same reported PPO hyperparameters unless otherwise stated and 10 random seeds for reproducibility.
- Results: Time-awareness significantly improves PPO on time-limited tasks and can produce behaviors such as Hopper-v1’s end-of-horizon “photo finish.”The learned Hopper-v1 behavior efficiently jumps forward before falling near the end of its allotted time.
- Results: Partial-episode bootstrapping significantly outperforms standard PPO on time-unlimited tasks and can reduce the negative impact of large experience replay buffers.On Hopper-v1, an agent trained with 200-step episodes learned to hop for at least 10^6 steps.
2. Time-awareness for time-limited tasks
For naturally time-limited tasks, the remaining time is part of the state and must be represented to preserve the Markov property. Experiments show that time-aware agents avoid state-aliasing errors and improve PPO performance, stability, and horizon-dependent behavior.
- Approach: Time-aware agents include the remaining time T −t in their state representation, allowing value functions and policies to depend on the finite horizon.The paper presents this as the appropriate treatment when time-limit terminations are part of the task.
- Motivation: Time-unaware agents treat states with different remaining times as identical, causing state aliasing and inconsistent value updates.This creates a partially observable problem and can produce suboptimal policies and training instability.
- Illustrative problems: In the Last Moment example, a time-aware agent stays for T −1 steps and then jumps, whereas a time-unaware agent cannot master the task for T > 1.The time-unaware optimum is to jump 50% of the time when T = 2 and never jump when T > 2.
- Illustrative problems: In the two-goal gridworld, time-awareness learns to pursue the closest reachable goal and stay when insufficient time remains, avoiding value leakage to unreachable states.The time-unaware policy always pursues the closest goal despite the remaining horizon.
- Illustrative problems: In Queue of Cars, time-aware PPO adapts the dangerous-action probability to both remaining time and distance to the goal, unlike standard PPO’s fixed position-based strategies.The figure reports that standard PPO learns various suboptimal strategies depending on initialization seeds.
- Standard control tasks: On multiple OpenAI Gym control tasks, time-aware PPO significantly improves performance and stability, with larger benefits at high discount factors.The comparison reports averaged rewards and standard errors over training steps; standard PPO may plateau or diverge, especially when γ = 1.
3. Partial-episode bootstrapping for time-unlimited tasks
For time-unlimited tasks, time limits should diversify experience rather than create environmental terminations. Partial-episode bootstrapping preserves continuation values, improving policy learning and reducing experience-replay instability.
- Motivation: Time limits used only to diversify experience should not be treated as environmental terminations.Treating them as terminal can produce conflicting value updates and forget rewards available after the timeout.
- Method: Partial-episode bootstrapping continues bootstrapping from the final non-terminal state when a timeout occurs.For one-step TD updates, the target is r + γˆvπ(s′) for non-environmental terminations, including timeouts.
- Continuous-control results: Partial-episode bootstrapping significantly outperforms standard PPO on Hopper-v1 and Walker2d-v1 while training on short interactions.Training partial episodes were limited to 300 time steps, whereas evaluation episodes were limited to 10^6 time steps.
- Continuous-control results: In InfiniteCubePusher-v0, partial-episode bootstrapping drastically outperformed standard PPO under short training limits and longer evaluation episodes.Training used 50-step episodes, while evaluation used 1000 steps to permit reaching several targets.
- Experience replay: In Difficult Gridworld, continuing to bootstrap at timeouts made learning much faster and greatly reduced the effect of replay-buffer size.Without proper timeout handling, experience replay significantly hurt performance.
4. Discussion
Time-awareness is necessary for correct credit assignment in finite-horizon tasks, but several practical conditions can let time-unaware agents perform relatively well. Partial-episode bootstrapping also depends on reliable value predictions and adequate exploration.
- Finite-horizon scope: Time-awareness is required for correct credit assignment when the objective is limited to a finite horizon.Time-unaware agents may still perform relatively well when timeouts are rare, observations correlate with time, repeated states at different remaining times are unlikely, or discounting reduces confusion.
- Finite-horizon scope: Observation histories, recurrent networks, and other POMDP methods may partly compensate when remaining time is omitted from the agent’s input.These approaches can help address partial observation but do not replace the paper’s finite-horizon time representation.
- Partial-episode bootstrapping: Partial-episode bootstrapping requires reliable value predictions, which generally depends on sufficient exploration.With fixed starting states and limited interactions, randomizing initial states can improve exploration of the state space.
- Partial-episode bootstrapping: Partial-episode bootstrapping is generic beyond time limits and can apply to other early termination causes.The supplied discussion presents this as a broader property of the approach.
5. Conclusion
The paper shows that time limits must be handled differently for time-limited and time-unlimited tasks to learn optimal policies reliably.
- Time-limited tasks require including the remaining time in the agent’s input.This avoids state aliasing and preserves the relevant state information.
- Time-unlimited tasks require continuing to bootstrap when partial episodes end because of time limits or other non-environmental terminations.This is necessary for correct value estimation.
- Both treatments significantly improve the performance of the evaluated reinforcement learning algorithms.