arXiv Machine Learning By Yunbei Xu

Indexed Bellman Information Complexity

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arXiv:2606. 11171v2 Announce Type: replace Abstract: We develop indexed Bellman information complexity, a representation-level theory of interactive decision making centered on information indices and reference histories.

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arXiv Machine Learning
Aug 19

The concentration game: Bayesian updating, regret, and information

The paper introduces a two-player zero-sum repeated game between a learner and nature that simultaneously captures Bayesian updating and an exact decomposition of exponential-weights regret. The game’s terminal payoff reflects the maximum gain a comparator can achieve given a fixed relative entropy from the prior, while the one-step constraint limits nature’s move by an information budget. The resulting regret splits into three precise components—per-round information loss, an additive retempering drift, and the comparator’s information relative to the prior—providing a unified framework that explains concentration phenomena, large-deviation bounds, and various learning methods such as bandits, posterior sampling, aggregation, and boosting.

By Akshay Balsubramani