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A novel bias expansion for two-timescale stochastic approximation reveals a $\varepsilon^2/\eta$ term that fundamentally alters extrapolation strategies.
Logarithmic regret is achieved in adaptive control of unknown, changing systems by exploiting the unique energy signatures of admissible plant changes during exploitation.
Discontinuous boundary dynamics no longer prevent finite-time guarantees in two-time-scale RL, unlocking rigorous $O(n^{-1}\log n)$ value-gap rates for projected actor-critic under dependent Markovian noise.
