The concentration game: Bayesian updating, regret, and information
We give a two-player zero-sum repeated game between a learner and nature whose value identity generates Bayesian updating and an exact accounting of exponential-weights regret at once, and supplies the comparator-class variational form that a wide class of concentration phenomena share. The terminal payoff is the most a comparator can gain at fixed relative entropy from the prior, and the one-step constraint is an information budget on nature's move under the learner's mixed action. With the learner's move otherwise unrestricted, Gibbs/Bayes weights emerge as its unique Bellman equalizer -- the mixed action that makes the per-round loss independent of which direction nature moves -- with ...
| Authors | Akshay Balsubramani |
|---|---|
| Primary category | cs.LG |
| Published | 18 August 2026 |
| Last updated at source | 18 August 2026 |
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