Normalization and effective learning rates in reinforcement learning (2407.01800v1)

Abstract: Normalization layers have recently experienced a renaissance in the deep reinforcement learning and continual learning literature, with several works highlighting diverse benefits such as improving loss landscape conditioning and combatting overestimation bias. However, normalization brings with it a subtle but important side effect: an equivalence between growth in the norm of the network parameters and decay in the effective learning rate. This becomes problematic in continual learning settings, where the resulting effective learning rate schedule may decay to near zero too quickly relative to the timescale of the learning problem. We propose to make the learning rate schedule explicit with a simple re-parameterization which we call Normalize-and-Project (NaP), which couples the insertion of normalization layers with weight projection, ensuring that the effective learning rate remains constant throughout training. This technique reveals itself as a powerful analytical tool to better understand learning rate schedules in deep reinforcement learning, and as a means of improving robustness to nonstationarity in synthetic plasticity loss benchmarks along with both the single-task and sequential variants of the Arcade Learning Environment. We also show that our approach can be easily applied to popular architectures such as ResNets and transformers while recovering and in some cases even slightly improving the performance of the base model in common stationary benchmarks.

Normalization and Effective Learning Rates in Reinforcement Learning

The paper "Normalization and Effective Learning Rates in Reinforcement Learning" by Clare Lyle et al. explores the subtle ramifications of normalization techniques on the learning dynamics in reinforcement learning (RL) algorithms. In particular, the authors identify a nuanced but significant interplay between normalization and effective learning rate, which has profound implications for network plasticity and performance in nonstationary environments.

Key Contributions

The primary contributions of the paper are:

• Layer Normalization Analysis: The paper provides an in-depth examination of the effects of layer normalization on neural network plasticity, showing how it aids recovery from saturated nonlinearities.
• Effective Learning Rate (ELR) Dynamics: It highlights the equivalence between parameter norm growth and effective learning rate decay, a phenomenon particularly detrimental in nonstationary continual learning settings.
• Normalize-and-Project (NaP): A novel methodology combining normalization with a mechanism to fix the effective learning rate by reparameterizing the model’s weight norms, ensuring stable learning dynamics.

Layer Normalization and Network Plasticity

The analysis begins by acknowledging prior work illustrating that maintaining plasticity—an RL network's ability to adapt to new information—is integral to performance. While normalization layers, like layer normalization, mitigate issues such as loss of plasticity and overestimation bias in deep RL, they are insufficient on their own. This insufficiency stems from the interaction between normalization and the learning rate, where the norm of the network parameters growing implicitly leads to a decay in the effective learning rate.

Layer normalization induces scale-invariance within the network, altering the gradient scaling and consequently the learning rate. The authors show that saturated units, which would otherwise cease learning, still receive gradient signals due to the correlations introduced by normalization, enabling recovery and continued learning—an important insight that supports the robustness of normalization techniques in RL tasks.

Effective Learning Rate Decay

A significant insight from this work is how parameter norm growth, a common occurrence in networks trained without regularization, leads to diminishing effective learning rates. This implicit learning rate decay is shown to be critical in certain stationary RL settings, explaining some counterintuitive findings such as performance degradation when weight decay is applied. The authors deduce that effective learning rate schedules have a more nuanced effect on optimization than previously understood.

The Normalize-and-Project (NaP) Method

To address the challenges identified, the paper introduces the Normalize-and-Project method. This technique couples the introduction of normalization layers with a weight projection step that maintains a constant effective learning rate. The NaP approach involves:

1. Adding normalization layers prior to nonlinearities.
2. Projecting the network’s weights onto a fixed-norm sphere after each update to disentangle the effective learning rate from parameter norm changes.

Empirical Evaluation

The authors validate NaP across multiple experiments, demonstrating that it does not impair performance on stationary supervised tasks while substantially improving robustness in nonstationary settings. Key results include:

• Continual Learning: NaP mitigates performance degradation seen with simple networks on the CIFAR-10 dataset under repeated label permutations, maintaining high accuracy over many cycles.
• Deep RL: In both single-task and sequential settings within the Arcade Learning Environment, NaP significantly improves performance and resilience to nonstationarity. The experiments indicated that without proper learning rate schedules, performance can still degrade, underscoring the delicate balance needed in managing learning rates.

Implications and Future Directions

The paper's findings suggest that ensuring stable and consistent learning rates is crucial for both theoretical understanding and practical implementation of RL algorithms. The proposed NaP method particularly shines in its simplicity and broad applicability to various architectures, including ResNets and transformers.

Future avenues for research include exploring adaptive learning rate schedules tailored for NaP, further dissecting the interaction between different normalization techniques and learning rates, and extending these insights to other forms of nonstationary problems beyond RL.

In conclusion, the paper by Lyle et al. presents compelling evidence for the intertwined roles of normalization and effective learning rates in deep learning, offering practical and theoretical advancements that could influence the design of more robust RL systems.