Online Algorithms via Minimax and Posterior Matching

• URL: http://arxiv.org/abs/2608.01616v1
• Date: Mon, 03 Aug 2026 02:46:17 GMT
• Title: Online Algorithms via Minimax and Posterior Matching
• Abstract summary: We develop a more unifying methodology via the minimax viewpoint.<n>We show that this single principle yields optimal or near-optimal guarantees for several classical online fractional problems.
• Score: 5.995574493969049
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Competitive analysis is central to the study of online algorithms, but upper bounds are often highly problem-specific. We develop a more unifying methodology via the minimax viewpoint. Guided by Yao's principle, we reduce worst-case competitive analysis to Bayesian online design under an arbitrary correlated prior over arrival sequences. For such a prior, let $X^*$ be the hindsight-optimal fractional solution for the realized instance, and let $X^{(t)}=\mathbb E[X^*\mid \mathcal F_t]$ be its posterior process. Our guiding rule is posterior matching: at each time $t$, choose the feasible online action that tracks the current posterior $X^{(t)}$ as closely as the online constraints permit. We show that this single principle yields optimal or near-optimal guarantees for several classical online fractional problems, including set cover, load balancing, matching and more general resource-allocation problems, recovering or improving state-of-the-art bounds in these settings with norm/concave objectives. Via known rounding reductions, it also yields randomized integral guarantees for weighted paging, MTS on star metrics, and ski-rental. At a technical level, our analysis reduces competitive guarantees to key probabilistic inequalities for the vector martingales generated by the posterior of the offline optimum. The resulting framework gives a reusable route from Bayesian online design under arbitrary correlated priors to information-theoretic worst-case competitive guarantees.

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