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A Dissection of Overfitting and Generalization in Continuous Reinforcement Learning

Amy Zhang, Nicolas Ballas, Joelle Pineau

arXiv:1806.07937v2cs.LGcs.AIstat.ML

TL;DR

Deep RL may overfit because many simulators provide limited training diversity, while existing overfitting tools largely come from supervised learning. The paper defines and diagnoses RL generalization, tests diverse simulated and natural-data settings, and finds that sufficient simulated diversity often supports generalization whereas natural observations produce more prominent overfitting.

  • Problem

    Existing overfitting analysis was developed mainly for supervised learning, leaving analogous generalization and memorization questions in deep RL, particularly continuous domains.

  • Method

    The paper evaluates within-task and out-of-task generalization using seed-based tests, expanded initial-state distributions, natural-data tasks, and training-diversity experiments.

  • Results

    Deep RL overfits in simulated and natural-image environments, but sufficient training diversity in simulation generally yields good generalization; overfitting is more prominent with natural data.

  • Takeaways & Limitations

    The findings support rigorous protocols and new benchmarks for defining, detecting, and reducing overfitting in deep RL.

  • Takeaways & Limitations

    Simulated environments remain necessary because RL sample complexity makes real-world development common, despite simulations lacking real-world diversity.

Abstract

from arXiv · show

The risks and perils of overfitting in machine learning are well known. However most of the treatment of this, including diagnostic tools and remedies, was developed for the supervised learning case. In this work, we aim to offer new perspectives on the characterization and prevention of overfitting in deep Reinforcement Learning (RL) methods, with a particular focus on continuous domains. We examine several aspects, such as how to define and diagnose overfitting in MDPs, and how to reduce risks by injecting sufficient training diversity. This work complements recent findings on the brittleness of deep RL methods and offers practical observations for RL researchers and practitioners.

1 Introduction

The paper examines whether deep RL exhibits memorization and poor generalization, especially in simulated and continuous domains. It develops tests and evaluates training diversity as a way to reduce overfitting.

  • Motivation: Deep RL can exhaust the limited noise in deterministic simulators, making memorization especially likely in simple tasks.These tasks often have small state spaces, simple perception, short planning horizons, and deterministic transitions.
  • Scope: The study investigates generalization versus memorization across model-free and model-based methods, discrete and continuous actions, and value-based and policy-based methods.Randomized reward experiments are also used to investigate memorization.
  • Approach: The authors test memorization and continuous-domain policy robustness by expanding initial-state distributions and adding stochastic observation noise.These interventions are intended to probe robustness beyond the original training conditions.
  • Experiments: Experiments cover classic discrete-action tasks, continuous-action MuJoCo environments, and new tasks whose observations come from natural images.The natural-image tasks examine generalization in settings closer to eventual real-world transfer.
  • Findings: Deep RL can overfit both standard simulators and natural-image tasks, while sufficient simulated training diversity often supports good generalization.Overfitting is more prominent with natural data, motivating new benchmarks for studying deep-RL overfitting.

2 Technical Background

The technical background introduces RL as policy optimization in MDPs and outlines value-based and policy-based deep-RL methods. It also describes fitted Q-iteration, DQN stabilization, and PPO for continuous actions.

  • Reinforcement Learning: An MDP is represented by state space, action space, transition distribution, reward function, initial-state distribution, and discount factor.A policy maps states to actions, and RL seeks a policy maximizing expected cumulative reward.
  • Value Functions: The value function is the expected discounted reward over a trajectory, while the Q-function evaluates state-action choices and can be estimated recursively.The Q-function is linked to Bellman’s equation.
  • Value-Based Methods: Without a known transition model, fitted Q-iteration estimates an approximate parameterized Q-function from a batch of data.This provides the basis for value-based learning from collected transitions.
  • Value-Based Methods: DQN extends fitted Q-iteration with a neural-network Q-function and stabilization techniques including target networks, replay, smoothing, and Double DQN.This approach is suited to continuous-state, discrete-action MDPs.
  • Policy-Based Methods: Policy-based methods directly estimate a parameterized neural-network policy that outputs an action distribution.PPO adds policy-change constraints, minibatches, and multiple learning epochs between environment queries.

3 Perspectives on generalization and overfitting

The paper adapts generalization and overfitting concepts from supervised learning to RL, distinguishing within-task from out-of-task evaluation. It focuses on continuous domains, where unseen initial states make generalization necessary.

  • 3.1 Generalization in Supervised Learning: Supervised-learning generalization compares true and expected error, while overfitting is poor generalization or a large generalization error.Because the true distribution is unavailable, practice uses a withheld test set from the same distribution.
  • 3.1 Generalization in Supervised Learning: Deep neural networks can memorize random supervised data, motivating the question of whether analogous memorization and overfitting arise in RL.The paper treats this as an open question for reinforcement-learning settings.
  • 3.2 Generalization and Memorization in Reinforcement Learning: The study focuses on continuous deep RL because function approximation is expected to be useful, yet the continuous state space prevents feasible exploration of every initial state.This makes generalization necessary for solving the task.
  • 3.2 Generalization and Memorization in Reinforcement Learning: Within-task generalization evaluates a policy on new trajectories from the same simulator, whereas out-of-task generalization evaluates it in another simulator setting.The distinction separates unseen trajectories from changed environment conditions.
  • 3.2 Generalization and Memorization in Reinforcement Learning: Because simulated randomness enters through random seeds, training and testing can be separated by using distinct seed-generated trajectory sets.The paper also identifies smaller datasets, varied seeds, and randomized simulator distributions as ways to examine generalization.
  • 3.2 Generalization and Memorization in Reinforcement Learning: The RL generalization evaluation uses training and test seeds, episode returns, and a parameterized policy; experiments fix the number of test seeds at M = 100.The policy is represented directly for policy-based methods and as the action maximizing Q for value-based methods.
  • 3.2 Generalization and Memorization in Reinforcement Learning: The paper adds natural-data tasks to study deep-RL generalization when noise comes from a natural source.This complements simulated-environment analyses with observations grounded in natural data.

4 Overfitting and memorization in the within-task case

Deep RL can overfit within-task training trajectories in discrete, continuous, and natural-image environments, while increasing training-seed diversity often improves generalization. Randomized-reward tests further show that RL can memorize environment-specific reward signals, especially with limited seeds.

  • 4.1 On the effect of the number of training random seeds: With around 10 training seeds, Acrobot has sufficient data diversity to generalize well in its simple environment.
  • 4.1 On the effect of the number of training random seeds: 4-dimensional Cartpole shows no overfitting, whereas Pixel Cartpole clearly overfits under the same seed-varying evaluation.
  • 4.1 On the effect of the number of training random seeds: Reacher generalizes well, while Thrower overfits with few training seeds but generalizes to 100 unseen goals from 5 seeds onward.
  • 4.1 On the effect of the number of training random seeds: ThrowerMulti requires more training diversity: adding five randomly located goal boxes produces overfitting even with 100 seeds and high test variance.
  • 4.1 On the effect of the number of training random seeds: Natural-image tasks retain a generalization gap even with 10k training images, with stronger overfitting than the baseline because one image yields multiple partially masked inputs.
  • 4.2 On memorization in RL: a randomized reward test: Randomized rewards expose memorization: one-seed agents can learn random rewards, whereas 100-seed agents more often concentrate on the true signal.
  • 4.2 On memorization in RL: a randomized reward test: Increasing reward-randomization probability prevents MNIST generalization while preserving perfect training-set memorization, requiring a ResNet-18 for the 10k-image case.

5 The out-of-task case for generalization in RL

The paper evaluates out-of-task generalization by shifting initial-state distributions and adding observation noise, finding that more training seeds improve generalization while distributional noise makes it harder.

  • Out-of-task evaluation changes transition dynamics, rewards, or initial-state distributions while keeping state and action sets fixed.
  • Initial-state shifts are created by multiplying the training initial state to form evaluation states, including strict-superset or nonoverlapping distributions.
  • More training seeds significantly improve Thrower generalization, whereas increased simulation-distribution noise makes generalization more difficult.
  • Table 1 reports Thrower estimated values averaged over 100 test seeds, with columns representing initial-state multipliers.
  • Observation robustness is measured by adding zero-mean Gaussian noise with variance σ2 to each observed state during evaluation.
  • Table 2 reports Thrower transfer results across variances σ2 of Gaussian observation noise, following a trend similar to the initial-state-shift experiments.

6 The effect of model-based RL

The paper tests whether model-based RL improves generalization by augmenting model-free architectures with learned next-state and reward predictions. In limited-seed settings, this instead compounds data bias and increases generalization error.

  • Model-based variants add next-state and reward prediction heads to Double DQN and modify PPO’s critic similarly.
  • Figure 8 varies training seeds from 1 to 100 for model-based Reacher and Thrower, averaging results over 5 runs.
  • Model-based learning compounds existing data bias when training uses few seeds.
  • Model-based Reacher exhibits generalization error where model-free Reacher did not, while Thrower’s generalization gap increases.

7 Related Work

Related work studies generalization in RL through simpler function approximators, theoretical error definitions, surveys, and discrete-domain memorization experiments. This paper focuses instead on continuous domains with effectively infinite state spaces.

  • Linear and RBF parameterizations achieved surprisingly good generalization, motivating calls for simpler models, although such models may not suit complex nonlinear dynamics.
  • Prior Q-learning work defines generalization error as the value difference between an optimal-policy evaluation and a learned greedy-policy evaluation.
  • A survey connects abstraction and generalization in RL with transfer, while noting that optimal-policy knowledge is infeasible in many environments.
  • Concurrent work examines memorization in discrete gridworlds, whereas this analysis targets continuous domains with effectively infinite states.

8 Conclusion

The conclusion argues that simulation-based RL needs rigorous methods to detect and combat overfitting, especially because simulated environments lack real-world diversity. The paper provides generalization metrics and practical lessons for transfer-sensitive settings.

  • Simulation lacks the complex signals, natural noise, and nonstationary stochasticity of real-world environments.
  • Natural-image experiments require more seeds for true generalization than simulation environments.
  • The paper presents overfitting-detection methodology and metrics for within-task and out-of-task generalization.
  • The methodology separates generalization evaluation from sample complexity for online methods.
  • The authors call for rigorous protocols to define, detect, and combat overfitting as deep RL models increase in capacity.

A Model Specifications and Hyperparameters

The experiments use separate multilayer perceptron and convolutional architectures for low-dimensional and pixel inputs, with input-dependent optimization and replay settings.

  • Pixel inputs use a convolutional head with 3 layers, middle dimension 512, and ReLU nonlinearities.
  • Learning rates are 3e-3 for low-dimensional inputs and 3e-4 for pixel inputs.
  • The target update interval is 1000, and the number of steps between updates is 2048.
  • Replay memory is 1M tuples for low-dimensional inputs and 100K tuples for pixel inputs.
  • Low-dimensional inputs use a 3-layer MLP with middle dimension 512.
  • Adam is used as the optimizer.

B.1.1 Random Reward

The random-reward experiments modify rewards by angular-state bins and vary the randomization probability, bin count, and training-seed count across Cartpole settings.

  • Random rewards bin the pole angle θ, assigning each bin probability p of receiving a multiplier sampled between -1 and 1.
  • The 4-Dim Cartpole experiments vary training seeds, bins b, and randomization probability p.
  • Figure 9 evaluates 4-dimensional Cartpole with k = 3 bins, p ∈ [0.1, 0.2, 0.5, 1], and the original reward.
  • The original Cartpole reward returns 1 at every step, and the passage reports good performance even when all k bins receive random multipliers.
  • The pixel Cartpole experiments also vary training seeds, bins b, and randomization probability p, using 10K episodes, 100K replay memory, and learning rate 3e-4.

B.2 Acrobot

The appendix describes Acrobot and related continuous-control experiments that randomize rewards by observation dimensions or angles, vary training conditions, and evaluate transfer under observation noise.

  • Acrobot: Acrobot is a two-link pendulum with only its second joint actuated; the objective is to raise the end-effector above the base by at least one link length.
  • Acrobot: Its state contains sine and cosine features for both joint angles plus joint angular velocities.
  • Acrobot: The action applies +1, 0, or -1 torque at the joint between the pendulum links.
  • Reward randomization: Acrobot reward randomization bins θ0, the first-link angle.
  • Experimental sweeps: Figures vary reward-randomization probability p, discount factor γ, and training-seed count across Acrobot, Reacher, Thrower, Cartpole, and model-based variants.
  • Reward randomization: Reacher reward randomization bins θ, the first-link angle, while another experiment bins the first observation-space dimension.
  • Transfer experiments: Transfer tables report performance across observation-noise variances σ2 for Cartpole, Pixel Cartpole, Acrobot, and Reacher.
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