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Convergence Analysis of Reinforcement Learning Agents. Srinivas Turaga 9.912 30th March, 2004. The Learning Algorithm. The Assumptions. Players use stochastic strategies. Players only observe their reward . Players attempt to estimate the value of choosing a particular action.

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## Convergence Analysis of Reinforcement Learning Agents

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**Convergence Analysis of Reinforcement Learning Agents**Srinivas Turaga 9.912 30th March, 2004**The Learning Algorithm**The Assumptions • Players use stochastic strategies. • Players only observe their reward. • Players attempt to estimate the value of choosing a particular action. The Algorithm • Play action i with probability Pr(i) • Observe reward r • Update value function v**The Learning Algorithm**Payoff matrix Player 2’s choice Player 1’s choice The Algorithm Value of action i • Play action iwith probability Pr(i) • Proportional to value of action i • Observe reward r • Depends on other player’s choice jalso • Update value function v • 2 simple schemes Algorithm 2 Algorithm 1 If action i chosen: If action i not chosen: forgetting no forgetting**Analysis Techniques**• Analysis of stochastic dynamics is hard! • So approximate: • Consider average case (deterministic) • Consider continuous time (differential equation) Random! Discrete time! Deterministic! Discrete time! Deterministic! Continuous time!**Results - Matching Pennies Game**• Analysis shows a fixed point corresponding to the Nash equilibrium. Linear stability analysis shows marginal stability. • Simulations of stochastic algorithm and deterministic dynamics diverge to corners. • Analysis shows a stable fixed point corresponding to matching behavior. • Simulations of stochastic algorithm and deterministic dynamics converge as expected.**Future Directions**• Validate approximation technique. • Analyze properties of more general reinforcement learners. • Consider situations with asymmetric learning rates. • Study behavior of algorithms for arbitrary payoff matrices.

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