High-Dimensional Continuous Control Using Generalized Advantage Estimation (1506.02438v6)

Abstract: Policy gradient methods are an appealing approach in reinforcement learning because they directly optimize the cumulative reward and can straightforwardly be used with nonlinear function approximators such as neural networks. The two main challenges are the large number of samples typically required, and the difficulty of obtaining stable and steady improvement despite the nonstationarity of the incoming data. We address the first challenge by using value functions to substantially reduce the variance of policy gradient estimates at the cost of some bias, with an exponentially-weighted estimator of the advantage function that is analogous to TD(lambda). We address the second challenge by using trust region optimization procedure for both the policy and the value function, which are represented by neural networks. Our approach yields strong empirical results on highly challenging 3D locomotion tasks, learning running gaits for bipedal and quadrupedal simulated robots, and learning a policy for getting the biped to stand up from starting out lying on the ground. In contrast to a body of prior work that uses hand-crafted policy representations, our neural network policies map directly from raw kinematics to joint torques. Our algorithm is fully model-free, and the amount of simulated experience required for the learning tasks on 3D bipeds corresponds to 1-2 weeks of real time.

• The paper introduces Generalized Advantage Estimation (GAE) which effectively reduces gradient variance and manages the bias-variance tradeoff in policy-gradient methods.
• The paper employs trust-region optimization to stabilize policy and value function updates during high-dimensional continuous control.
• The empirical results on cart-pole, bipedal, and quadrupedal tasks validate GAE’s ability to improve sample efficiency and overall control performance.

High-Dimensional Continuous Control Using Generalized Advantage Estimation

In the field of reinforcement learning (RL), policy gradient methods are particularly appealing due to their inherent ability to optimize cumulative reward directly and their compatibility with nonlinear function approximators, such as neural networks. However, these methods traditionally face challenges related to sample efficiency and stability, impacted by high variance in gradient estimates and the nonstationarity of incoming data. To mitigate these issues, this paper proposes a method called Generalized Advantage Estimation (GAE), which aims to reduce variance in policy gradient estimates while managing the bias-variance tradeoff effectively.

Key Contributions

1. Generalized Advantage Estimation (GAE): The GAE is an estimator schema parameterized by $\gamma \in [0,1]$ and $\lambda \in [0,1]$. This estimator significantly reduces variance by weighting value function estimates to balance bias introduced by this variance reduction. The paper positions GAE within the context of existing methods such as TD($\lambda$) and highlights its general application potential across both online and batch RL settings.
2. Trust-Region Optimization: For robust and stable learning, the paper employs trust-region methods to optimize both the policy and value function. By doing so, it ensures steady improvement by constraining the updates within a region around the current parameter values to prevent drastic changes, thus dampening the effects of nonstationarity.
3. Empirical Validation: The methodology is validated through a series of experiments on 3D locomotion tasks which involve learning complex motor skills for bipedal and quadrupedal simulated robots. The results demonstrate the efficacy of GAE in learning high-dimensional continuous control tasks using neural network policies for torque-level control.

Experimental Results and Analysis

Cart-Pole Balancing Task

For the classic cart-pole task, using an intermediate value of $\lambda$ (specifically in the range of [0.92, 0.98]) in the GAE framework resulted in faster policy improvement. This makes a strong case for the effectiveness of generalized advantage locations by appropriately adjusting the bias-variance tradeoff.

3D Locomotion Tasks

Bipedal Locomotion:

Experiments on a simulated 3D biped demonstrated that intermediate values of $\gamma$ ([0.99, 0.995]) and $\lambda$ ([0.96, 0.99]) yielded the most stable and efficient learning curves. The resulting gaits were stable and efficient, indicating the model's robustness.

Quadrupedal Locomotion and Biped Standing:

For quadrupedal locomotion, the GAE framework with $\lambda = 0.96$ showed superior performance over other configurations. Similarly, in the bipedal standing task, utilizing a value function was essential for success, with $\lambda$ values of both 0.96 and 1 showing comparable efficacy.

Theoretical Implications and Future Directions

1. Bias-Variance Tradeoff in Advantage Estimation: The paper’s exploration of the bias-variance tradeoff through $\gamma$ and $\lambda$ parameters provides a nuanced understanding. $\gamma$ generally introduces systemic bias, while $\lambda$ manages the bias when the value function is inaccurate, suggesting that lower values of $\lambda$ could offer optimal performance due to minimal bias introduction.
2. Value Function Optimization: The use of trust-region methods to optimize the value function represents a critical advancement. This ensures that the value function remains robust and does not overfit to recent data.
3. Shared Function Architecture: A potential area for further research is exploring shared architectures for policy and value functions. This could leverage overlapping features in the input data, potentially accelerating learning and improving performance.
4. Comparison with Alternative Methods: Future studies should further investigate and compare the GAE framework with emerging actor-critic methods that utilize continuous-valued action differentiation, particularly in high-dimensional spaces similar to those addressed in this paper.

Practical Implications

The practical implications of this research are profound. By substantially improving sample efficiency and stability in policy gradient methods, GAE paves the way for real-world applications where data collection is expensive or time-consuming. Additionally, the successful demonstration of learning high-dimensional control policies warrants exploration in autonomous robots and complex system controls, where traditional RL methods have been less effective.

In conclusion, this paper presents a significant advancement in reinforcement learning for continuous control problems, particularly by addressing sample efficiency and stability issues through Generalized Advantage Estimation and trust-region optimization. The empirical results substantiate the proposed methods, highlighting their practical and theoretical value. Further exploration and extension of this work could significantly impact the broader field of RL and its applications in real-world autonomous systems.