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Synthetic Monitoring Environments for Reinforcement Learning

Leonard Pleiss, Carolin Schmidt, Maximilian Schiffer

TL;DR

It is shown that SMEs offer a standardized, transparent testbed for transitioning RL evaluation from empirical benchmarking toward rigorous scientific analysis, and how specific environmental properties - such as action or state space size, reward sparsity and complexity of the optimal policy - impact WD and OOD performance.

Abstract

Reinforcement Learning (RL) lacks benchmarks that enable precise, white-box diagnostics of agent behavior. Current environments often entangle complexity factors and lack ground-truth optimality metrics, making it difficult to isolate why algorithms fail. We introduce Synthetic Monitoring Environments (SMEs), an infinite suite of continuous control tasks. SMEs provide fully configurable task characteristics and known optimal policies. As such, SMEs allow for the exact calculation of instantaneous regret. Their rigorous geometric state space bounds allow for systematic within-distribution (WD) and out-of-distribution (OOD) evaluation. We demonstrate the framework's benefit through multidimensional ablations of PPO, TD3, and SAC, revealing how specific environmental properties - such as action or state space size, reward sparsity and complexity of the optimal policy - impact WD and OOD performance. We thereby show that SMEs offer a standardized, transparent testbed for transitioning RL evaluation from empirical benchmarking toward rigorous scientific analysis.

Synthetic Monitoring Environments for Reinforcement Learning

TL;DR

It is shown that SMEs offer a standardized, transparent testbed for transitioning RL evaluation from empirical benchmarking toward rigorous scientific analysis, and how specific environmental properties - such as action or state space size, reward sparsity and complexity of the optimal policy - impact WD and OOD performance.

Abstract

Reinforcement Learning (RL) lacks benchmarks that enable precise, white-box diagnostics of agent behavior. Current environments often entangle complexity factors and lack ground-truth optimality metrics, making it difficult to isolate why algorithms fail. We introduce Synthetic Monitoring Environments (SMEs), an infinite suite of continuous control tasks. SMEs provide fully configurable task characteristics and known optimal policies. As such, SMEs allow for the exact calculation of instantaneous regret. Their rigorous geometric state space bounds allow for systematic within-distribution (WD) and out-of-distribution (OOD) evaluation. We demonstrate the framework's benefit through multidimensional ablations of PPO, TD3, and SAC, revealing how specific environmental properties - such as action or state space size, reward sparsity and complexity of the optimal policy - impact WD and OOD performance. We thereby show that SMEs offer a standardized, transparent testbed for transitioning RL evaluation from empirical benchmarking toward rigorous scientific analysis.
Paper Structure (42 sections, 4 theorems, 12 equations, 7 figures, 1 table)

This paper contains 42 sections, 4 theorems, 12 equations, 7 figures, 1 table.

Table of Contents

  1. Introduction
  2. Related work
  3. Contribution
  4. Synthetic monitoring environments
  5. Methodology
  6. Transition kernel
  7. Affine transformation
  8. Triangle wave activations
  9. Optimal policy
  10. The uniform layer
  11. The full network
  12. Reward Formulation and Episode Dynamics
  13. Step reward calculation
  14. Reward distribution and state augmentation
  15. Termination and truncation
  16. ...and 27 more sections

Key Result

Theorem 1

Let $X \in \mathbb{R}^n$ be a random vector representing the input with independent components $X_i \sim \mathcal{U}(0,1)$. Let $T: \mathbb{R}^n \to \mathbb{R}^m$ be a layer of the optimal policy mapping defined as $T(X) = \Phi(W(X - \mathbf{\mu}))$, where $\mu_i = 0.5$, $\Phi$ is the standard norma

Figures (7)

  • Figure 1: Topological deformation of the input space as a function of the number of stacked uniform layers, $\mathcal{C}_{\pi^{\star}}$.
  • Figure 2: Ablations for PPO, SAC and TD3 across different task configurations over $10$ seeds. Curves indicate median evaluation performance, smoothed over $10$ points. Shaded areas indicate interquartile ranges.
  • Figure 3: Evaluation performance during training (column 1) and final within-distribution and out-of-distribution performance for PPO, SAC and TD3 across different complexities of the optimal policy the agent seeks to mirror ($\mathcal{C}_{\pi^{\star}}$, columns 2-4). Performance is defined as the complement of the mean average error between action and optimal action $\tilde{r}_t$. States within $\mathbb{R}^2(0,1)$ are within-distribution. States beyond the unit square are out-of-distribution. SD = State Dimension.
  • Figure 4: Performance by proximity to the training distribution for PPO, SAC and TD3 across 10 seeds. Alg. = Algorithm, WD = Within-distribution, OOD = Out-of-distribution, MAE = Mean Average Error.
  • Figure 5: Optimal action distribution under varying input dimensions $N_s$ and complexities $\mathcal{C}_{\pi^{\star}}$ for $10{,}000$ states, uniformly sampled from the unit hypercube that bounds the state space. AD = Action dimension.
  • ...and 2 more figures

Theorems & Definitions (8)

  • Theorem 1: Asymptotic preservation of the uniform measure
  • proof
  • Theorem 2: Exact preservation of uniform measure
  • proof
  • Proposition 1: Action mass preservation
  • proof
  • Proposition 2: Bounded variance transfer
  • proof