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A Study on Overfitting in Deep Reinforcement Learning

Chiyuan Zhang, Oriol Vinyals, Remi Munos, Samy Bengio

arXiv:1804.06893v2cs.LGstat.ML

TL;DR

Deep RL’s increasing capacity creates a need to understand whether agents generalize beyond their training environments. This paper systematically studies standard agents in controlled maze tasks and finds that they can overfit robustly, with test performance varying drastically despite optimal training rewards.

  • Problem

    Deep RL lacks standard separated training and testing protocols and systematic evidence about generalization, although agents are increasingly applied to important real-world problems.

  • Method

    The paper systematically evaluates standard deep RL agents on controlled maze environments using disjoint training and test levels, including regular and randomized tasks.

  • Results

    Agents memorize many training mazes and can have drastically different test performance despite the same optimal training performance; stochasticity does not necessarily prevent or detect overfitting.

  • Takeaways & Limitations

    Carefully separated training and validation or test sets are recommended because stochasticity-based evaluation may leave overfitting undetected.

  • Takeaways & Limitations

    Formal characterizations of inductive bias that are both mathematically tractable and broadly applicable remain an open problem.

Abstract

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Recent years have witnessed significant progresses in deep Reinforcement Learning (RL). Empowered with large scale neural networks, carefully designed architectures, novel training algorithms and massively parallel computing devices, researchers are able to attack many challenging RL problems. However, in machine learning, more training power comes with a potential risk of more overfitting. As deep RL techniques are being applied to critical problems such as healthcare and finance, it is important to understand the generalization behaviors of the trained agents. In this paper, we conduct a systematic study of standard RL agents and find that they could overfit in various ways. Moreover, overfitting could happen "robustly": commonly used techniques in RL that add stochasticity do not necessarily prevent or detect overfitting. In particular, the same agents and learning algorithms could have drastically different test performance, even when all of them achieve optimal rewards during training. The observations call for more principled and careful evaluation protocols in RL. We conclude with a general discussion on overfitting in RL and a study of the generalization behaviors from the perspective of inductive bias.

1 Introduction

Deep RL’s growing capacity raises unresolved concerns about overfitting and generalization because standard evaluation often lacks separated training and test stages. This paper systematically studies these behaviors and finds memorization, sharply varying test performance, and robust overfitting despite stochasticity.

  • High-capacity models and extended training can increase overfitting risk, making controlled training and evaluation important for out-of-sample generalization.
  • Deep RL lacks systematic theoretical and empirical studies of generalization, complicating understanding, reproduction, and comparison of reported results.
  • Because RL commonly omits separate training and testing stages, training performance may not reflect performance on unseen but statistically similar environments.
  • The paper systematically studies standard deep RL agents using a configurable maze environment spanning different task difficulties and regularities.
  • Agents can memorize many regular and random training mazes while achieving optimal training rewards but drastically different test performance.
  • Added environmental stochasticity does not necessarily prevent or reveal overfitting, which the study characterizes as robust.
  • The paper interprets varying generalization behavior through inductive bias and supports this interpretation with empirical studies.

2 Related Work

Prior RL research provides theoretical generalization analyses and empirical evaluation proposals, but deep RL remains less theoretically understood and difficult to compare empirically. This paper extends randomization-based capacity studies to deep RL while emphasizing generalization and overfitting.

  • Theoretical work has characterized generalization through bandit, contextual decision-process, RL, and PAC analyses.
  • Deep neural networks have enabled empirical successes in large-scale discrete and continuous-control RL, while theoretical understanding remains comparatively limited.
  • Earlier evaluation proposals used separate training and testing trajectories or multiple environments, but some omitted action selection and exploration components.
  • This study adapts supervised-learning randomization tests to RL, evaluating memorization of random tasks while focusing on generalization and overfitting rather than new algorithmic performance.

3 Generalization in Deep RL Agents

The study evaluates deep RL agents on controlled gridworld mazes using isolated training and test levels, then examines how training duration, dataset size, task difficulty, and reward randomization affect generalization. Agents can reach optimal training rewards while generalizing very differently and retaining substantial memorization capacity under random rewards.

  • 3 Generalization in Deep RL Agents: The evaluation models each task as an episodic MDP and measures non-discounted episode rewards separately on disjoint training and test initial-state sets.
  • 3.1 Task Setup and Evaluation Protocol: The controlled environment uses BASIC, BLOCKS, and TUNNEL mazes with increasing difficulty and fixes the maximum episode reward at 2.1.
  • 3.1 Task Setup and Evaluation Protocol: A3C workers asynchronously update a parameter server, while a separate test worker evaluates current policies on isolated test levels without sending gradients.
  • 3.2 Training Optimality and Generalization: Training compares 10, 100, 1,000, and 10,000 training levels across the three maze difficulties while continuously tracking training and test rewards.
  • 3.2 Training Optimality and Generalization: Test rewards generally increase with more training levels and decrease with maze difficulty, although training rewards reach the optimum in every case.
  • 3.3 Memorization Capacity of Deep RL Agents: With reward signs independently flipped on training levels, small datasets still yield near-optimal training performance, while larger datasets expose capacity limits more strongly in TUNNEL mazes.
  • 3.3 Memorization Capacity of Deep RL Agents: Even under heavy reward noise, agents achieve non-trivial training rewards, producing a large training–testing gap.
  • 3.3 Memorization Capacity of Deep RL Agents: The agents memorize a non-trivial number of random-reward training levels, so identical architectures, methods, and near-optimal training rewards can yield drastically different test performance.

4 Evaluation of Generalization in Deep RL

Training-set rewards alone can be misleading: deep RL agents may generalize poorly despite optimal training performance, and common stochastic evaluations may fail to reveal this overfitting.

  • Separate training and testing environments are needed because training rewards may not reflect performance on unseen scenarios.
  • Random starts slightly improve test performance, but agents can still fit even random training levels almost optimally.
  • Sticky actions with ζ = 0.25 produce results very similar to random starts alone, including when both regularizers are combined.
  • Overfitted agents retain high training-set evaluation scores under sticky actions, random starts, or both, despite poor test performance.
  • Sticky actions barely distinguish agents with drastically different generalization, even across stickiness levels and action types.
  • Stochasticity can help identify determinism-exploiting algorithms like Brute but does not reliably prevent or detect overfitting in deep RL agents.

5 Discussions on Overfitting in RL

Overfitting in deep RL takes multiple forms, including robust memorization that survives environmental stochasticity. The paper therefore connects generalization to inductive bias and emphasizes separate evaluation sets and standardized protocols.

  • Deep RL agents can fit random noises and overfit robustly even when trained with regularizers that add environmental stochasticity.
  • Neural-network agents may remain overfitted under stochastic evaluation because their gradient-trained black-box policies can acquire implicit robustness.
  • Exploration-exploitation imbalance resembles overfitting when agents specialize in part of the state space, but insufficient exploration can instead resemble underfitting.
  • Deep RL optimization can remain difficult and unstable because commonly used gradient-based algorithms lack convergence guarantees.
  • Memorization is not always undesirable: specialized subroutines can improve efficiency, although they may generalize poorly to small perturbations.
  • The paper interprets varied generalization through inductive bias and recommends statistically tied training and validation or testing sets.

6 Inductive Bias of Algorithms and Problems

The study interprets generalization through inductive bias: MLPs fit training levels better, while ConvNets generalize better on regular mazes with spatially invariant rewards. Increased capacity preserves ConvNets’ generalization advantage, but formal characterization of compatible inductive bias remains open.

  • Deep RL agents can memorize large random training sets while still generalizing well on regular mazes.
  • ConvNets consistently outperform MLPs on test performance when maze rewards are regular and spatially invariant.
  • MLPs fit training levels better than ConvNets but generalize worse, especially when the task’s spatial regularity favors convolutional inductive bias.
  • With added capacity, Big-ConvNets no longer underperform MLPs on randomized training mazes while retaining better generalization on low-noise regular games.
  • Formalizing inductive bias in a mathematically tractable way that covers diverse real-world problems remains an open problem.

7 Conclusion

The paper concludes that over-parameterized deep RL agents can memorize random training data, while generalization depends on compatibility between algorithmic inductive bias and task structure. It recommends careful evaluation because stochasticity may not reveal robust overfitting.

  • Large neural networks and powerful training algorithms can memorize large random training sets in deep RL.
  • Good generalization can still occur when an algorithm’s inductive bias matches the task, although formal characterization remains challenging.
  • Stochasticity-based evaluation may fail to detect overfitting, so training and test data should be isolated even in noisy environments.

A.1 Task Setup

The study uses a configurable 2D gridworld maze in which agents collect positively rewarded objects, avoid negatively rewarded objects, and terminate by collecting a key. Reward randomization tests independently flip object-reward signs.

  • The maze is a 2D gridworld with five object types, including positive-reward objects, negative-reward objects, and a terminating object.
  • An oracle agent can achieve an episode reward of 2.1, while timeout and obstacle penalties reduce rewards for unsuccessful behavior.
  • Randomization tests independently flip each object’s reward sign and rescale rewards to preserve the maximum episode reward of 2.1.
  • Agents receive a multi-channel image input and use an A3C policy head with five discrete actions.

A.2 Training Protocol and Dataset Splitting

Training uses episodic A3C with randomized maze resets, separate finite pools of training and testing level IDs, and a test worker that evaluates without updating parameters. The protocol supports continuous held-out evaluation during training.

  • Each worker interacts with an environment copy, updates shared parameters asynchronously, and resets to a new random maze after every episode.
  • Training and testing use separate finite pools of level IDs, with each level ID determining its initial state through a pseudorandom seed.
  • Random starts and sticky actions were tested as training regularizers or evaluation strategies on BLOCKS and TUNNEL mazes.
  • The test worker runs on held-out levels without computing gradients, enabling continuous test-performance curves during training.
  • The study varies network families and runs 20 training jobs per setting to filter failures caused by unlucky random initialization.
  • The A3C setup uses four training workers, one non-updating test worker, clipped rewards, 15-step unrolls, entropy regularization, and RMSProp.

B Additional Experimental Results

Random starts and sticky actions affect evaluation differently across maze difficulty and training-set size. Regularization can improve test scores, but serious overfitting remains, and held-out performance may diverge from training-set evaluations.

  • Combining random starts and sticky actions makes fitting many random BLOCKS8 mazes harder, but does not significantly change training scores on harder TUNNEL mazes.
  • Regularization improves test scores on TUNNEL mazes, yet serious overfitting remains.
  • With small training sets or random mazes, test performance differs substantially from training-set performance under added stochasticity.
  • For BASIC mazes without noise, 100 training levels suffice for similar evaluation performance, whereas TUNNEL mazes require more than 1,000.
  • Figure 7 compares evaluation protocols across BASIC, BLOCKS, and TUNNEL mazes for agents trained on 10, 100, 1,000, or 10,000 mazes.

C Analysis of Agent Trajectories

Trajectory visualizations examine how trained agents behave under stochasticity and evaluation perturbations. They illustrate robust local memorization, failures under larger state changes, and the limits of visual evidence for quantitative conclusions.

  • Agents trained on small datasets can memorize a soft lookup table for training levels without understanding maze dynamics.
  • Soft memorization tolerates small perturbations, so stochastic policies and sticky actions may fail to detect it, whereas remote random starts can expose it.
  • Agents trained on large datasets with random rewards can still overfit while learning the underlying maze dynamics, allowing random-start robustness.
  • Agent-1, trained on only 10 levels, produces similar trajectories on one training maze with small stochastic variations.
  • Trajectory visualizations use segmented frames, obstacle and object markers, colored time ordering, and cumulative rewards to depict episodes.
  • The authors state that conclusions rely mainly on quantitative results because individual stochastic rollouts may be good or bad by chance and representative mazes were cherry-picked.
  • On an unseen test maze, Agent-1 remains near its initial corner until timeout, unlike its successful training-maze trajectory.

C.2 Behaviors of an Overfitted Agent

Agent-1 overfits its 10 training levels: it performs well on training mazes and tolerates sticky actions, but fails on unseen mazes and random starts. Larger training sets support more robust navigation, even under random rewards.

  • Agent-1 struggles on an unseen test maze and times out after 200 steps, while behaving near-optimally on a training maze.
  • On the same training maze, sticky actions with stickiness 0.25 preserve Agent-1’s optimal reward, but random starts leave it ineffective throughout the episode.
  • Agent-1 overfits to 10 levels without developing good maze understanding; sticky actions create only local perturbations that its stochastic rollouts may already cover.
  • Agent-2, trained on 10,000 levels, handles random-start configurations that trap Agent-1, although it may skip a potentially beneficial object.
  • Sticky actions can accidentally move an agent into a negative-reward object, substantially lowering final reward even when the remaining episode is optimal.
  • Agent-3, trained on 1,000 random-reward levels, memorizes the training set yet learns navigation well enough to handle random starts.
  • Random starts impose larger perturbations than sticky actions, but both evaluation strategies involve task-dependent trade-offs; held-out tests are more direct.

D Different Levels and Types of Action Stickiness

The study compares default and alternative sticky-action definitions across stickiness levels. Agents remain robust under the default mode, while the alternative mode can collapse performance without distinguishing generalization quality.

  • Agent-1 reaches optimal rewards relatively easily with stickiness 0.99 despite having no sticky-action training experience.
  • The proposed robustness explanation is that consecutive frames are usually semantically close, making stale actions suitable for both states.
  • The alternative sticky-action mode carries executed actions across frames, potentially applying stale actions in states farther from the original state.
  • With alternative-mode stickiness 0.99, all agents fail because the environment executes the initial default stay action almost continuously.
  • Default-mode scores decline only slightly, whereas alternative-mode scores become negative at high stickiness.
  • Across both sticky-action modes, evaluation curves remain nearly identical as training levels increase, so stickiness fails to distinguish generalization power.
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