Mixing Makes Markovian Contexts Cheap for Linear Bandits

The paper extends the idea that contexts are cheap for linear bandits from i.i.d. settings to Markovian context processes. By assuming uniform geometric ergodicity, the authors construct a stationary surrogate action set and use a delayed‑update scheme to mitigate bias from nonstationary conditional context distributions. They provide a phased algorithm for unknown stationary distributions and achieve high‑probability regret bounds comparable to standard linear bandit oracles in fast‑mixing regimes, with empirical validation showing gains over LinUCB.

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