Unmodified linear Q-learning converges in L2 to a bounded set at a polynomial or exponential rate under an epsilon-softmax behavior policy with adaptive temperature.
A Markovian decision process
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Linear $Q$-Learning Does Not Diverge in $L^2$: Convergence Rates to a Bounded Set
Unmodified linear Q-learning converges in L2 to a bounded set at a polynomial or exponential rate under an epsilon-softmax behavior policy with adaptive temperature.