Step Sizing and Trust Regions

Last updated: December 15, 2024

1. Introduction

In previous lessons, we explored the limitations of foundational on-policy methods like Vanilla Policy Gradient (VPG), A3C, and Generalized Advantage Estimation (GAE). While these approaches introduced techniques to reduce variance and stabilize training, they struggle to ensure reliable policy updates.

To address this, we introduced the concept of a surrogate loss, which simplifies optimization by providing a more stable objective. However, key questions remain:

How can we ensure updates move in the right direction without destabilizing the policy?
How do we guarantee consistent progress without risking catastrophic degradation?

These challenges lead us to step-sizing and trust regions. Properly controlling policy updates prevents poor adjustments and maintains stability. This lesson highlights the importance of step-sizing in reinforcement learning, its unique challenges compared to supervised learning, and introduces the Trust Region Policy Optimization (TRPO) algorithm, a milestone in stabilizing on-policy methods.

2. Why Step Size Matters

2a. What Is Step Size?

Step size determines how far the policy is updated along the gradient direction. While the gradient indicates the best local direction for improvement, it doesn’t specify how far to move. Selecting the right step size is critical:

Too Small: Slows progress, requiring many updates for noticeable improvement.
Too Large: Risks overshooting the optimal policy, causing instability or failure.

2b. Why Is Step Sizing Necessary?

Gradient-based updates are only reliable within a limited range. Moving too far invalidates the gradient’s approximation, leading to harmful updates instead of beneficial ones.

2c. Key Challenges of Step Sizing

First-Order Approximation Limitations:
Gradients are local approximations and don’t account for non-linearities or constraints. Large steps assume the gradient direction remains accurate, which isn’t true beyond a small neighborhood.
Differences Between Supervised Learning and RL:
- Supervised Learning: Bad step sizes are recoverable because the dataset is fixed, allowing the model to learn from consistent data in subsequent updates.
- Reinforcement Learning: Poor updates lead to degraded policies, which collect low-quality data, creating a feedback loop that prevents recovery and stalls learning.
Bad Step Sizes in RL:
- Wasted resources on poor updates or interactions under suboptimal policies.
- Catastrophic degradation requiring complete retraining or inefficient recovery methods like shrinking the step size.

2d. Simplest Approach: Line Search

A simple method for step sizing is line search, which tests various step sizes by evaluating their performance through rollouts. While straightforward, this approach has significant drawbacks:

Computational Expense: Requires multiple evaluations along the line, increasing training time.
Naivety: Ignores where the gradient approximation is reliable, often leading to suboptimal updates.

2e. A More Sophisticated Approach

More advanced methods incorporate concepts like the surrogate loss, which leverage additional policy structure information to make better-informed decisions about step sizes. These approaches provide a balance between computational efficiency and effective policy improvement, avoiding the pitfalls of naive techniques.

2f. Consequences of Poor Step Sizing

Cascading Errors: A single bad update degrades the policy, leading to suboptimal data and amplified errors.
Irrecoverable Policies: Unlike supervised learning, RL lacks a static dataset, so a degraded policy may stall learning entirely.
Wasted Resources: Poor updates waste time and compute on flawed data collection and restarts.

3. Supervised Learning vs. Reinforcement Learning: A Comparison

Step sizing and trust regions are more critical in RL due to its dynamic data collection. The table below highlights the key differences:

Aspect	Supervised Learning	Reinforcement Learning
Static vs. Dynamic Data	Static dataset allows recovery from bad steps.	Policy affects data collection, amplifying bad steps.
Impact of a Bad Update	Easily corrected in subsequent steps.	Degrades policies, leading to poor data.
Recovery	Consistent data refines the model.	Often requires retraining or smaller steps.

4. Addressing the Challenge

Challenges like cascading errors, irrecoverable policies, and wasted resources demand robust solutions. Trust regions provide a principled way to ensure stable and meaningful policy updates.

4a. What Is a Trust Region?

A trust region is a neighborhood around the current policy where the gradient-based approximation of policy improvement remains reliable. Restricting updates within this region helps:

Avoid Catastrophic Updates: Prevent extreme policy changes that degrade performance.
Stabilize Learning: Ensure consistent improvements by staying within bounds where the surrogate loss is valid.

Unlike trial-and-error step sizing, trust regions provide a structured method for safe and significant updates. This is crucial in RL, where policy updates directly influence data quality.

4b. Why Trust Regions Matter

Consistency: Bounded updates reduce destabilizing steps.
Efficiency: Minimize restarts and hyperparameter tuning.
Theoretical Guarantees: Ensure updates reliably improve the policy.

Trust regions underpin TRPO, an advanced algorithm that formalizes these principles to stabilize on-policy methods by balancing improvement and safety.

5. Summary

In the next lesson, we’ll dive into TRPO, exploring its theoretical foundations, implementation, and how it resolves the challenges of naive step sizing. TRPO represents a significant step forward in achieving reliable and efficient learning in on-policy RL.