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Exact Formulas for Finite-Time Estimation Errors of Decentralized Temporal Difference Learning with Linear Function Approximation

arXiv 2204.09801 ↗First posted 20 Apr 2022cs.LG cs.SY eess.SYcited by 0

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Abstract (arXiv)

In this paper, we consider the policy evaluation problem in multi-agent reinforcement learning (MARL) and derive exact closed-form formulas for the finite-time mean-squared estimation errors of decentralized temporal difference (TD) learning with linear function approximation. Our analysis hinges upon the fact that the decentralized TD learning method can be viewed as a Markov jump linear system (MJLS). Then standard MJLS theory can be applied to quantify the mean and covariance matrix of the estimation error of the decentralized TD method at every time step. Various implications of our exact formulas on the algorithm performance are also discussed. An interesting finding is that under a necessary and sufficient stability condition, the mean-squared TD estimation error will converge to an exact limit at a specific exponential rate.

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References · 19

  1. 2019Multi-Agent Reinforcement Learning: A Selective Overview of Theories and Algorithmscited by 555
  2. 2018A Finite Time Analysis of Temporal Difference Learning With Linear Function Approximationcited by 225
  3. 2019Finite-Time Error Bounds For Linear Stochastic Approximation and TD Learningcited by 165
  4. 2014Analysis and Design of Optimization Algorithms via Integral Quadratic Constraintscited by 105
  5. 2019Two Time-scale Off-Policy TD Learning: Non-asymptotic Analysis over Markovian Samplescited by 31
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  8. 2019Characterizing the Exact Behaviors of Temporal Difference Learning Algorithms Using Markov Jump Linear System Theorycited by 17
  9. 2019Finite-Time Performance of Distributed Temporal Difference Learning with Linear Function Approximationcited by 14
  10. 2019A Unified Switching System Perspective and O.D.E. Analysis of Q-Learning Algorithmscited by 14
  11. 2017Analysis of Biased Stochastic Gradient Descent Using Sequential Semidefinite Programscited by 10
  12. 2013Distributed Reinforcement Learning via Gossipcited by 8
7 more
  1. 2019Analysis and Design of First-Order Distributed Optimization Algorithms over Time-Varying Graphscited by 7
  2. 2019A frequency-domain analysis of inexact gradient methodscited by 7
  3. 2017A Unified Analysis of Stochastic Optimization Methods Using Jump System Theory and Quadratic Constraintscited by 6
  4. 2019Robustness of accelerated first-order algorithms for strongly convex optimization problemscited by 6
  5. 2018Dissipativity Theory for Accelerating Stochastic Variance Reduction: A Unified Analysis of SVRG and Katyusha Using Semidefinite Programscited by 3
  6. 2022Convex Programs and Lyapunov Functions for Reinforcement Learning: A Unified Perspective on the Analysis of Value-Based Methodscited by 3
  7. 2019A Control-Theoretic Approach to Analysis and Parameter Selection of Douglas-Rachford Splittingcited by 2

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