• Corpus ID: 234767752

A Discrete-Time Switching System Analysis of Q-learning

@inproceedings{Lee2021ADS,
  title={A Discrete-Time Switching System Analysis of Q-learning},
  author={Donghwan Lee and Jianghai Hu and Niao He},
  year={2021}
}
This paper develops a novel control-theoretic framework to analyze the non-asymptotic convergence of Q-learning. We show that the dynamics of asynchronous Q-learning with a constant step-size can be naturally formulated as a discrete-time stochastic affine switching system. Moreover, the evolution of the Q-learning estimation error is over- and underestimated by trajectories of two simpler dynamical systems. Based on these two systems, we derive a new finite-time error bound of asynchronous Q… 

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References

SHOWING 1-10 OF 21 REFERENCES
Sample Complexity of Asynchronous Q-Learning: Sharper Analysis and Variance Reduction
TLDR
The above bound improves upon the state-of-the-art result by a factor of at least 1 up to some logarithmic factor, provided that a proper constant learning rate is adopted.
Error bounds for constant step-size Q-learning
Double Q-learning
TLDR
An alternative way to approximate the maximum expected value for any set of random variables is introduced and the obtained double estimator method is shown to sometimes underestimate rather than overestimate themaximum expected value.
A Unified Switching System Perspective and Convergence Analysis of Q-Learning Algorithms
TLDR
It is shown that the nonlinear ODE models associated with Q-learning and many of its variants can be naturally formulated as affine switching systems.
A Lyapunov Theory for Finite-Sample Guarantees of Asynchronous Q-Learning and TD-Learning Variants
This paper develops an unified framework to study finite-sample convergence guarantees of a large class of value-based asynchronous reinforcement learning (RL) algorithms. We do this by first
Finite-Time Analysis of Asynchronous Stochastic Approximation and Q-Learning
TLDR
A general asynchronous Stochastic Approximation scheme featuring a weighted infinity-norm contractive operator is considered, and a bound on its finite-time convergence rate on a single trajectory is proved.
Stochastic approximation with cone-contractive operators: Sharp 𝓁∞-bounds for Q-learning
TLDR
These results show that relative to model-based Q-iteration, the `∞-based sample complexity of Q-learning is suboptimal in terms of the discount factor γ, and it is shown via simulation that the dependence of the bounds cannot be improved in a worst-case sense.
Nonlinear Systems
Nonlinearity is ubiquitous in physical phenomena. Fluid and plasma mechanics, gas dynamics, elasticity, relativity, chemical reactions, combustion, ecology, biomechanics, and many, many other
Speedy Q-Learning
We introduce a new convergent variant of Q-learning, called speedy Q-learning (SQL), to address the problem of slow convergence in the standard form of the Q-learning algorithm. We prove a PAC bound
Stability and Stabilizability of Switched Linear Systems: A Survey of Recent Results
TLDR
This paper focuses on the stability analysis for switched linear systems under arbitrary switching, and highlights necessary and sufficient conditions for asymptotic stability.
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