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Towards Generalization and Simplicity in Continuous Control
Aravind Rajeswaran, Kendall Lowrey, Emanuel Todorov, Sham Kakade
TL;DR
The paper examines whether complex policy architectures are necessary for continuous-control benchmarks and studies how training conditions affect robustness. It trains simple linear and RBF policies with natural policy gradients, finding strong benchmark performance and more robust behavior under diverse initial-state distributions. The authors conclude that complex architectures should not be the default without comparisons against simpler alternatives, while noting that the benchmarks cannot determine the ideal architecture.
Problem
The relative contributions of policy representation, optimization, and task design remain insufficiently understood, while benchmark tasks may not reveal the ideal control architecture.
Method
The paper trains linear and RBF policies with natural policy gradients on Gym-v1 MuJoCo continuous-control tasks and evaluates robustness under diverse training conditions.
Results
Simple linear and RBF parameterizations solve many benchmark tasks without significant performance loss, while diverse initial-state training produces robust policies.
Takeaways & Limitations
Complex policy architectures should not be the default choice unless side-by-side comparisons with simpler alternatives support them.
Takeaways & Limitations
The work does not attempt to provide a definitive answer about the ideal control architecture because the current benchmark tasks are insufficient for that question.
Abstract
from arXiv · showhide
This work shows that policies with simple linear and RBF parameterizations can be trained to solve a variety of continuous control tasks, including the OpenAI gym benchmarks. The performance of these trained policies are competitive with state of the art results, obtained with more elaborate parameterizations such as fully connected neural networks. Furthermore, existing training and testing scenarios are shown to be very limited and prone to over-fitting, thus giving rise to only trajectory-centric policies. Training with a diverse initial state distribution is shown to produce more global policies with better generalization. This allows for interactive control scenarios where the system recovers from large on-line perturbations; as shown in the supplementary video.
1 Introduction
The paper asks which simple ingredients suffice for continuous-control benchmarks, challenging the assumption that complex neural architectures are necessary. It argues that simple policies can perform strongly while exposing brittleness in conventional training and testing.
- Motivation: Recent reinforcement-learning progress has left the relative contributions of representation, optimization, and task design insufficiently understood.The paper frames simple approaches as necessary baselines for understanding these factors.
- Motivation: The study asks what simplest set of ingredients can succeed on popular Gym-v1 continuous-control benchmarks.These tasks involve under-actuation, contact dynamics, and high-dimensional continuous spaces.
- Representation: Linear and RBF policies achieve state-of-the-art results on widely studied tasks while linear policies train almost 20x faster.Their faster training is attributed to orders of magnitude fewer parameters.
- Robustness: Conventional training can learn a walking limit cycle yet fail to recover from delivered perturbations, revealing brittle behavior.The paper identifies this brittleness as undesirable for transferring reinforcement learning to robotics.
- Robustness: More diverse training conditions are used to learn robust policies, but the benchmark results provide no compelling evidence favoring multi-layer architectures.The paper also evaluates learned policies interactively to examine robustness.
- Scope: The work does not provide a definitive answer about the ideal control architecture because current benchmark tasks are insufficient for that question.The authors call for revisiting architecture comparisons as the field progresses.
2 Problem Formulation and Methods
The paper formulates average-reward continuous-control problems and trains simple parameterized stochastic policies with natural policy gradients. It compares linear policies with RBF-feature policies, using trajectory-based gradient and advantage estimates.
- 2 Problem Formulation and Methods: The task is modeled as an average-reward Markov Decision Process with continuous states, actions, rewards, stochastic transitions, and an initial-state distribution.
- 2 Problem Formulation and Methods: Finite-length simulation rollouts approximate the infinite-horizon objective and define finite-horizon value, Q, and advantage functions.
- 2.1 Algorithm: Natural policy gradient training collects trajectories, computes policy-log-probability gradients and advantages, forms the Fisher matrix, updates policy parameters, and fits the value function.
- 2.1 Algorithm: The natural-gradient update selects the steepest ascent direction under a Fisher-information constraint rather than using the vanilla gradient direction.
- 2.1 Algorithm: Normalized Fisher-metric steps are used because fixed learning rates are difficult to tune across reward scales; the reported experiments use δ = 0.05.
- 2.1 Algorithm: GAE estimates advantages by learning a value function, while avoiding reuse of the same trajectory batch for value fitting and policy-gradient estimation.
- 2.2 Policy Architecture: The linear policy maps observations directly to motor torques and learns W, b, and σ; observations include joint positions, velocities, and sometimes contact information.
- 2.2 Policy Architecture: The RBF policy enriches the linear representation with random Fourier features, using random weights, a bandwidth parameter, and random phase shifts before learning the output parameters.
3 Results on OpenAI gym-v1 benchmarks
Linear and RBF policies perform competitively on OpenAI Gym continuous-control benchmarks, while conventional benchmark design can produce trajectory-centric policies that fail under perturbations.
- Linear policies are competitive on most tasks, while RBF policies outperform previous results on five of six considered tasks.
- Linear and RBF policies learn faster on four of the six tasks under the reported reward-threshold comparison.The threshold is 90% of the final score achieved by the stochastic linear policy.
- Narrow initial-state distributions and termination conditions make benchmark policies trajectory-centric and vulnerable to small perturbations.The walker can fall after small perturbations and cannot get up, while the swimmer cannot turn after its heading changes.
- Figure 1 compares stochastic Linear and RBF learning curves with TRPO-trained neural-network rewards, averaging results across three random seeds.
- The simulated robots are complex, but the benchmark notion of success is described as inadequate for evaluating broader control behavior.
4 Modified Tasks and Results
Modified tasks broaden initial states, adjust rewards and termination conditions, and alter physics to test whether simple policies can learn recovery and resist perturbations.
- The modified tasks target representational limits and global policies that remain robust across diverse states and perturbations.
- Wider initial-state distributions require skills such as getting up, walking, and turning to be learned together and retained.Examples include prone walker starts and randomized swimmer or ant heading angles.
- Reward shaping supports the broadened initial states, while the modified tasks remove all Gym-v1 termination conditions.
- The modified physics reduce action ability or increase mass, making agents more under-actuated and producing more realistic motion.
- The modifications require progress toward reward maximization together with recovery from adverse conditions and resistance to perturbations.In the modified hopper task, the agent gets up before hopping forward.
- Figure 4 compares distance traveled after perturbations across training configurations with termination conditions, no termination, and diverse initialization.Swimmer perturbations change heading angle, while walker and hopper receive an external force for 0.5 seconds.
- On the modified walker, increasing Fourier features increases expressiveness and score; 500 features perform best, followed by the fully connected neural network.The linear policy makes forward progress and can get up but does not learn as efficient a walking gait.
5 Summary and Discussion
The paper examines representation, task modeling, and optimization, finding that simple policies can solve benchmark tasks while robustness depends strongly on training conditions.
- Representation: Linear and RBF policies solve varied continuous-control tasks, challenging the assumed need for multi-layer neural networks.The authors frame this as evidence that expressive approximators are not necessary for the studied testbeds.
- Modeling: Diverse initial-state distributions are sufficient to train robust policies, whereas narrow distributions produce elaborate but brittle behaviors.The paper treats initial-state distributions and rewards as researcher-designed assumptions that affect solution quality.
- Optimization: REINFORCE is sensitive to hyperparameters, while natural-gradient preconditioning improves learning but trades computation against wall-clock performance.The authors suggest intermediate conjugate-gradient effort, such as 20 steps, can be favorable for large-scale problems.
- Related considerations: Linear function approximation offers convergence guarantees and error bounds in many dynamic-programming methods, unlike nonlinear approximation, which can diverge in many cases.The passage presents this as a motivation for side-by-side comparisons between simple and complex architectures.
6 Conclusion
The paper concludes that simple policy parameterizations solve many benchmark tasks without significant performance loss, including global task variants requiring competence across more states.
- 6 Conclusion: Simple policy parameterizations solve many benchmark continuous-control tasks without significant performance loss.The conclusion argues that complex architectures should not be default choices without comparisons against simpler alternatives.
- 6 Conclusion: Global task variants require policies to handle a much larger set of states, and simple representations remain sufficient in these cases.The authors connect these results to the need for simplicity and generalization in reinforcement learning.
A Choice of Step Size
The paper compares normalized and un-normalized natural-policy-gradient step sizes, finding normalized steps easier to apply across tasks while un-normalized choices are problem-specific.
- A Choice of Step Size: Normalized step sizes solve an optimization problem using a dimensionless step parameter δ, whereas un-normalized updates use α.The distinction is tied to the units of the learning-rate parameters.
- A Choice of Step Size: Un-normalized α scales inversely with reward, making it difficult to tune and requiring task- and phase-specific rescaling.The authors report that fixed α values or schedules were difficult to choose.
- A Choice of Step Size: The same normalized step size δ works across swimmer, hopper, and walker, while task-specific un-normalized values often cause divergence elsewhere.The figure includes divergence cases such as α = 0.25 for walker.
B Effect of GAE
The paper evaluates GAE’s bias–variance trade-off and finds that low-variance estimates accelerate early learning, while low-bias estimates improve asymptotic performance.
- B Effect of GAE: GAE interpolates between temporal-difference and Monte Carlo advantage estimates through λ, trading bias against variance.λ = 0 gives a high-bias, low-variance estimate, while λ = 1 gives a low-bias, high-variance estimate.
- B Effect of GAE: Smaller λ values make fast initial progress, but larger λ values achieve better asymptotic performance after the initial phase.Even λ = 1 provides good asymptotic performance, while GAE can retain faster initial learning.