Core Concepts

Optimistic Q-learning algorithm achieves sample efficiency in RL without modeling transition probabilities.

Abstract

Authors study sample complexity of online Q-learning with partial dynamics knowledge.
Focus on systems evolving with additive disturbance model.
Algorithm achieves regret without S and A dependency.
Comparison with other Q-learning algorithms.
Empirical results show convergence to optimal policy.
Discussion on horizon dependency, value function assumptions, noise in model, continuous spaces, and future directions.

Stats

We present an optimistic Q-learning method that achieves ˜O(POLY(H)√T) regret under perfect knowledge of f, where T is the total number of interactions with the system.
Our algorithm can learn an approximately optimal policy in a number of samples independent of state and action spaces if only a noisy estimate ˆf of f is available.
The regret of using asymptotically accurate online estimators with our algorithm is ˜O(√H6T + L√HdT).

Quotes

"Our algorithm achieves sample efficiency in RL without explicitly modeling transition probabilities."

Key Insights Distilled From

by Meshal Alhar... at **arxiv.org** 03-28-2024

Deeper Inquiries

In continuous spaces, the algorithm's performance can be enhanced by incorporating techniques such as discretization and leveraging the metric inherited from the continuous space. By discretizing the continuous space appropriately and ensuring that the metric is preserved, the algorithm can be applied effectively. Additionally, ensuring that the algorithm accounts for the approximation errors introduced by discretization and maintains accuracy in the value function estimates is crucial for optimal performance in continuous spaces. Furthermore, exploring variance reduction techniques and optimizing the bonus design to suit the continuous space setting can also contribute to improving the algorithm's performance.

The noise structure in the approximate model can have significant implications on regret in the algorithm. When there is noise in the approximate model, it introduces bias and inaccuracies in the estimation of the true function, leading to suboptimal policies and increased regret. The level of noise in the approximate model directly impacts the sub-optimality gap and the convergence of the algorithm to the optimal policy. Higher levels of noise can result in larger regret values and slower convergence to the optimal policy. Therefore, minimizing noise in the approximate model is essential to reduce regret and improve the algorithm's performance.

To extend the algorithm to handle value function approximation in continuous spaces, several modifications and considerations need to be taken into account. Firstly, the algorithm should incorporate techniques for discretizing the continuous space while preserving the metric to ensure accurate representation of the continuous environment. Additionally, the algorithm should be adapted to account for approximation errors introduced by discretization and ensure that the value function estimates are optimized for continuous spaces. Techniques such as function approximation methods like neural networks or kernel methods can be employed to approximate the value function in continuous spaces. By integrating these modifications and techniques, the algorithm can effectively handle value function approximation in continuous spaces and provide optimal policies in such environments.

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