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Towards General-Purpose Model-Free Reinforcement Learning

Scott Fujimoto, Pierluca D'Oro, Amy Zhang, Yuandong Tian, Michael Rabbat

arXiv:2501.16142v1cs.LGcs.AI

TL;DR

RL algorithms are often specialized to particular tasks, while model-based approaches bring complexity and computational overhead. MR.Q uses model-based representations in a model-free algorithm and performs competitively across diverse benchmarks without changing its algorithm or hyperparameters. The authors frame it as a step toward general-purpose model-free deep RL, while noting limits in task settings and evaluation scope.

  • Problem

    Many RL algorithms require task-specific choices and hyperparameters, while model-based methods add complexity and computational cost.

    Source: §1 · p. 2

  • Method

    MR.Q learns representations that approximately linearize the value function, using unified state-action embeddings without planning or simulated trajectories.

    Source: §1 · p. 2

  • Results

    MR.Q performs competitively against domain-specific and general baselines across four benchmarks and 118 environments without algorithmic or hyperparameter changes.

    Source: §1 · p. 2

  • Takeaways & Limitations

    MR.Q demonstrates that model-free deep RL is a promising route to strong performance across environments with less complexity and expense than model-based alternatives.

    Source: §6 · p. 10

    MR.Q is not equipped for hard-exploration or non-Markovian settings, and its evaluation covers only standard RL benchmarks.

    Source: §6 · p. 10

Abstract

from arXiv · show

Reinforcement learning (RL) promises a framework for near-universal problem-solving. In practice however, RL algorithms are often tailored to specific benchmarks, relying on carefully tuned hyperparameters and algorithmic choices. Recently, powerful model-based RL methods have shown impressive general results across benchmarks but come at the cost of increased complexity and slow run times, limiting their broader applicability. In this paper, we attempt to find a unifying model-free deep RL algorithm that can address a diverse class of domains and problem settings. To achieve this, we leverage model-based representations that approximately linearize the value function, taking advantage of the denser task objectives used by model-based RL while avoiding the costs associated with planning or simulated trajectories. We evaluate our algorithm, MR.Q, on a variety of common RL benchmarks with a single set of hyperparameters and show a competitive performance against domain-specific and general baselines, providing a concrete step towards building general-purpose model-free deep RL algorithms.

1 INTRODUCTION

RL has a general-purpose premise, but practical algorithms are specialized by task and input type. The paper asks whether model-based representations can support a general model-free algorithm, then evaluates MR.Q across benchmarks without changing its algorithm or hyperparameters.

1 INTRODUCTION

  • Most RL algorithms are specialized by action and observation type, with each category requiring distinct algorithmic choices and hyperparameters.Table 1 compares Rainbow and TD3; their shared hyperparameters have more differences than similarities.Source: §1 · p. 2, Table 1 · p. 2
  • General-purpose model-based methods have shown strong benchmark performance without retuning, but their complexity and computational cost limit practicality.The paper proposes a model-free approach intended to retain model-based performance and sample efficiency without planning overhead.Source: §1 · p. 2
  • The paper asks whether model-based representations alone can enable sample-efficient general-purpose learning.Its hypothesis is that model-based objectives benefit learning through their implicitly learned representations rather than the model itself.Source: §1 · p. 2
  • MR.Q maps states and actions into a unified embedding, aiming to remove environment-specific input characteristics and standardize hyperparameters.Its features approximately capture a linear relationship between state-action pairs and value.Source: §1 · p. 2
  • MR.Q achieves competitive performance against domain-specific and general baselines across four benchmarks and 118 environments without algorithmic or hyperparameter changes.The proposed approach learns features that approximately capture a linear relationship between state-action pairs and value.Source: §1 · p. 2

2 RELATED WORK

Related work contrasts general-purpose methods and benchmark-specialized deep RL with dynamics-based representations. MR.Q draws on representation-learning and abstraction ideas while differing from related methods in its inputs and training losses.

General-purpose RL

  • Traditional general-purpose methods include evolutionary and policy-gradient approaches, but they can have poor sample efficiency and be prone to local minima.Policy-gradient and evolutionary methods offer update rules with convergence guarantees and input-space independence (Williams, 1992; Sutton et al., 1999; Schulman et al., 2015; 2017).Source: §2 · pp. 2–3
  • Deep RL commonly favors benchmark-specific algorithms, while generalizing beyond initial benchmarks can require engineering, tuning, or algorithmic discovery.DreamerV3 demonstrated performance across benchmarks without retuning but used costly large models and simulated rollouts (Hafner et al., 2023).Source: §2 · p. 3

Dynamics-based representation learning

  • Dynamics-based representations use system dynamics for adaptation, partial observability, and feature selection; MR.Q discards the original input and adds reward and termination losses.MR.Q is closely related to TD7 and also uses multi-step returns, unrolled dynamics, and categorical losses.Source: §2 · p. 3

Related theoretical connections

  • Linear spectral representation seeks a low-rank transition decomposition and a linear embedding–value relationship, while two-stage linear RL learns a nonlinear embedding for linear RL.Source: §2 · p. 3

State abstraction

  • State abstraction methods use reward and dynamics similarity to abstract states or actions, inspiring practical representation-shaping approximations in deep RL.Source: §2 · p. 3

3 BACKGROUND

The background defines an MDP and the value function used by value-based RL. It also establishes notation for approximate values and target networks.

3 BACKGROUND

  • An MDP is defined by state and action spaces, dynamics, rewards, and a discount factor.Source: §3 · p. 3
  • A value function Qπ(s,a) is the expected discounted sum of rewards from state s and action a when following policy π.Source: §3 · p. 3
  • The approximate value function is Qθ, and target-network parameters Qθ′ are periodically synchronized with current parameters to introduce stationarity in prediction targets.Source: §3 · p. 3

4 MODEL-BASED REPRESENTATIONS FOR Q-LEARNING

MR.Q learns embeddings with model-based objectives to approximate a linear value representation while using model-free Q-learning. The theory motivates practical safeguards, and the algorithm trains the encoder, value function, and policy separately.

4.1 THEORETICAL MOTIVATION

  • The model-free and model-based approaches converge to the same fixed point, and value error is bounded by the accuracy of estimated reward and dynamics.Source: §4.1 · p. 4
  • Policy-conditioned targets are non-stationary, while joint feature and dynamics optimization risks trivial minima under sparse rewards or incomplete coverage; state-only targets and target encoders address these issues.The target encoder is periodically updated to track the current encoder, though the modified objective no longer guarantees convergence to a fixed point.Source: §4.1 · p. 5
  • A suitable MDP homomorphism allows a nonlinear function over embeddings to represent Qπ and preserve a corresponding optimal policy.Source: §4.1 · p. 5

4.2 ALGORITHM

  • MR.Q learns state-action embeddings approximately linear with the true value function, then uses a nonlinear value function to account for approximation error.The state encoder can be swapped for different input modalities, while downstream networks operate on the resulting vector embedding.Source: §4.2 · p. 6

4.2.1 ENCODER

  • The encoder loss unrolls reward, dynamics, and terminal predictions over a short horizon; reward uses categorical prediction, while dynamics and terminal signals use mean-squared error.The dynamics target is the next-state embedding from a target encoder, avoiding dependence on the current policy.Source: §4.2.1 · pp. 6–7

4.2.2 VALUE FUNCTION

  • TD3-style twin critics use minimum target values, multi-step returns, Huber loss, and replay-buffer reward normalization to keep loss scales consistent across benchmarks.Source: §4.2.2 · p. 7

4.2.3 POLICY

  • Deterministic policy gradients use Gumbel-Softmax for discrete actions and Tanh for continuous actions, with added action noise for exploration.Source: §4.2.3 · p. 7
  • Figure 2 shows per-benchmark average learning curves over 10 seeds with 95% stratified-bootstrap intervals; 500k DMC steps correspond to 1M frames and 2.5M Atari steps to 10M frames.Source: Figure 2 · p. 8

5 EXPERIMENTS

Across four benchmarks, MR.Q is evaluated against domain-specific and general baselines using fixed hyperparameters. Results show strong cross-benchmark performance, while design variants expose benchmark-dependent effects.

5 EXPERIMENTS

  • MR.Q is compared with strong domain-specific and general baselines across four popular benchmarks, with baseline defaults fixed across environments.The stated objective is broad applicability across diverse tasks rather than state-of-the-art performance on any single benchmark.Source: §5 · p. 8

5.1 MAIN RESULTS

  • The evaluation covers Gym locomotion, proprioceptive and visual DMC, and Atari, spanning continuous low-dimensional state inputs, image inputs, and discrete actions.The reported sets include 5 Gym locomotion tasks, 28 tasks in each DMC benchmark, and 57 Atari games.Source: §5.1 · p. 8
  • MR.Q leads both DMC benchmarks and all continuous-control benchmarks overall, trails TD7 slightly on Gym, and loses to DreamerV3 on Atari while surpassing PPO, DQN, and Rainbow.The authors note that DreamerV3 uses a model with 40 times more parameters and comparatively struggles on the other benchmarks.Source: §5.1 · p. 9

5.2 DESIGN STUDY

  • Non-linear model capacity increases do not improve performance, while MSE reward loss and No unroll help moderately on Gym but significantly hurt Atari.The authors interpret these results as evidence that approximate value linearity can matter more than added capacity and that hyperparameters can overfit individual benchmarks.Source: Table 2 · p. 9, §5.2 · p. 10

6 DISCUSSION AND CONCLUSION

MR.Q performs strongly across diverse benchmarks, while the discussion argues that model-free deep RL can offer high performance with less complexity and cost than model-based alternatives. The authors also find weak positive transfer across benchmarks and identify settings and evaluation domains beyond the study’s scope.

6 DISCUSSION AND CONCLUSION

  • The paper presents MR.Q as a simpler, less expensive model-free approach that achieves strong performance across diverse benchmarks and environments.The authors frame it as a first step toward general-purpose model-free deep RL.Source: §6 · p. 10
  • The authors report insights into which design choices matter for general-purpose model-free deep RL and how common benchmarks respond to them.They also argue that simpler general-purpose algorithms could make deep RL more accessible to a wider audience.Source: §6 · p. 10
  • MR.Q integrates model-based objectives with a model-free backbone; the authors suggest representations may matter more than planning, which adds execution time, complexity, and tuning.They note that more complex settings may be needed to reliably see benefits from model-based search or planning.Source: §6 · p. 10
  • Top performers often fail to transfer between benchmarks, including across Gym and DMC despite shared tasks and the same MuJoCo simulator.The discussion says this limits what single-benchmark evaluations can establish and points to a need for more comprehensive benchmarks.Source: §6 · p. 10
  • MR.Q is not equipped for hard-exploration tasks or non-Markovian environments, and its evaluation covers only standard RL benchmarks.The authors note that demonstrating versatility in settings such as team video games, drone racing, and large language models requires testing beyond this study’s scope.Source: §6 · p. 10

A PROOFS

The proofs relate model-free and model-based value solutions in linear representations. They also establish conditions under which a latent model preserves the true value function and bound value error by estimated dynamics and reward accuracy.

A PROOFS

  • Theorem 1 states that the fixed point of the model-free approach and the model-based solution are the same.The proof derives the model-free fixed point from the linear semi-gradient TD update and relates it to the model-based solution.Source: A PROOFS · pp. 19–20
  • Theorem 2 bounds the value error of the shared solution by the accuracy of the estimated dynamics and reward.The proof relates value error recursively to the discounted state-action visitation distribution.Source: A PROOFS · pp. 20–21
  • Theorem 3 states that, under its latent-model conditions and a corresponding policy, a function over state-action embeddings can equal the true value function.The proof also states that an optimal policy exists in the embedding space corresponding to the original optimal policy.Source: A PROOFS · pp. 21–22

B EXPERIMENTAL DETAILS

The appendix reports MR.Q hyperparameter values held fixed across all benchmarks.

B EXPERIMENTAL DETAILS

  • MR.Q hyperparameter values are kept fixed across all benchmarks.The table caption identifies the settings as MR.Q hyperparameters.Source: Table 3 · p. 23

B.2 NETWORK ARCHITECTURE

The appendix describes MR.Q’s encoder and network components, then specifies evaluation procedures and benchmark configurations for Gym, DM Control, and Atari.

B.2 NETWORK ARCHITECTURE

  • The state encoder and state-action encoder are trained end-to-end as one network, while value and policy networks are trained independently from the encoders.The state embedding also feeds the policy without propagating gradients; the state-action embedding predicts reward, next-state embedding, and terminal signal, and feeds the value network without propagating gradients.Source: §B.2 · pp. 24–25
  • The state encoder uses a CNN for image inputs and an MLP for vector inputs; the state-action encoder combines processed actions with state embeddings.The value network is a four-layer MLP, and the policy network is a three-layer MLP with output activation depending on whether actions are discrete or continuous.Source: §B.2 · pp. 24–25

B.3 ENVIRONMENTS

  • Main experiments use 10 seeds, average performance over 10 evaluation episodes, and evaluate Gym and DM Control every 5k steps and Atari every 100k steps.The design study uses 5 seeds.Source: §B.3 · p. 26
  • The evaluation specifies five common Gym locomotion tasks, 28 default DM Control tasks, and 57 Atari-57 games, with benchmark-specific preprocessing and normalization.For Atari, two games are omitted for DQN and Rainbow because they are missing from the Dopamine framework.Source: §B.3 · p. 26

B.4 BASELINES

The appendix describes how comparison baselines were evaluated and lists the software versions used. Baseline results came from author-reported scores, reruns, or named frameworks, depending on the method and benchmark.

B.4 BASELINES

  • DreamerV3 results for Gym and DMC were rerun over 10 seeds with DMC-benchmark hyperparameters and slight protocol changes, while Atari results used the authors’ reported scores.Source: §B.4 · p. 28
  • DrQ-v2 results were author-reported where possible and rerun for missing results; DQN and Rainbow results came from Dopamine, while PPO used Stable Baselines 3 with default hyperparameters and policies.Source: §B.4 · p. 28
  • TD-MPC2 results came from reruns using author-suggested defaults over 10 seeds, with separate code branches for Gym and DMC; TD7 results came from authors or reruns using Gym-benchmark defaults.Source: §B.4 · p. 28

B.5 SOFTWARE VERSIONS

  • The listed software versions are Gymnasium 0.29.1, MuJoCo 3.2.2, NumPy 2.1.1, Python 3.11.8, and PyTorch 2.4.1.Source: §B.5 · p. 28

C COMPLETE MAIN RESULTS

The section presents benchmark results across Gym locomotion, proprioceptive and visual DMC, and Atari. Captions specify evaluation budgets, aggregation measures, seeds, and confidence intervals, but do not provide comparative scores for every visual.

C.1 GYM

  • Table 4 reports Gym locomotion final average performance at 1M time steps over 10 seeds, aggregating TD3-normalized scores with mean, median, IQM, and 95% bootstrap intervals.Source: Table 4 · p. 29

C.2 DMC - PROPRIOCEPTIVE

  • Table 5 reports DMC proprioceptive final average performance at 500k time steps, equivalent to 1M original-environment time steps, using default rewards and 95% bootstrap intervals over 10 seeds.Source: Table 5 · p. 30

C.3 DMC - VISUAL

  • Figure 5 shows DMC visual learning curves over environment interactions, where 500k time steps equal 1M original-environment frames; results use 10 seeds and shaded 95% bootstrap intervals.Source: Figure 5 · p. 33

C.4 ATARI

  • Table 7 reports Atari final average performance at 2.5M time steps, equivalent to 10M original-environment frames, using human-normalized scores and 95% bootstrap intervals over 10 seeds.Source: Table 7 · p. 34

D COMPLETE ABLATION RESULTS

The ablation appendix defines how differences are normalized and highlighted, then lists the Gym design variants included in the study.

D COMPLETE ABLATION RESULTS

  • Ablation tables give per-environment raw scores and aggregate mean, median, and IQM over normalized-score differences; highlighting encodes difference ranges.Gym scores are normalized using TD3.Source: D COMPLETE ABLATION RESULTS · p. 36

D.1 GYM

  • Gym ablations compare MR.Q with a linear value function, a dynamics target, and no target encoder.Source: §D.1 · p. 36
  • Other Gym variants revert the nonlinear model or use MSE reward loss.Source: §D.1 · p. 36
  • The remaining Gym ablations remove reward scaling, the minimum, or LAP, and compare removing MR, using a 1-step return, or omitting unroll.Source: §D.1 · p. 36

D.2 DMC - PROPRIOCEPTIVE

The complete ablation results cover proprioceptive DMC, visual DMC, and Atari, listing design variants alongside per-task results and aggregate summaries.

D.2 DMC - PROPRIOCEPTIVE

  • Proprioceptive DMC ablations cover value-function, dynamics-target, target-encoder, model, reward-loss, reward-scaling, minimum, LAP, MR, return-horizon, and unroll variants, with aggregate summaries reported.Source: §D.2 · pp. 37–38

D.3 DMC - VISUAL

  • Visual DMC tables list value-function, dynamics-target, target-encoder, model, reward-loss, reward-scaling, minimum, LAP, MR, return-horizon, and unroll variants with aggregate summaries.Source: §D.3 · pp. 39–40

D.4 ATARI

  • The Atari ablations include per-game scores and aggregate summaries for value-function, dynamics-target, and target-encoder variants.Source: §D.4 · pp. 41, 44
  • Further Atari tables report per-game results and aggregate summaries for reverting the nonlinear model and using MSE reward loss.Source: §D.4 · pp. 41–42
  • Additional Atari comparisons report per-game results and aggregate summaries for removing reward scaling, the minimum, or LAP.Source: §D.4 · p. 43
  • The final Atari ablations compare removing MR, using a 1-step return, or omitting unroll.Source: §D.4 · p. 44
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