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No Coin Left Behind: Maximizing Strategic Surplus Against No-Regret Dynamics
[Submitted on 6 Apr 2026 (v1), last revised 21 May 2026 (this ve · 2026-05-25 · via cs.LG updates on arXiv.org

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Abstract:We investigate the strategic surplus obtainable against a Follow-the-Regularized-Leader (FTRL) learner with constant step size $\eta$ in $n\times m$ two-player zero-sum games played over $T$ rounds against a clairvoyant optimizer. In contrast with prior analysis, we show that the extraction of such regret-scale surplus is an inherent feature of the FTRL family, rather than an artifact of specific instantiations. First, for a fixed max-min optimizer, we establish a sweeping law of order $\Omega(N_{\mathrm{sub}}/\eta)$, proving that utility surplus scales with the number of the learner's suboptimal actions $N$ and vanishes in their absence. Second, for an alternating optimizer, a surplus of $\Omega(\eta T/\mathrm{poly}(n,m))$ can be guaranteed regardless of the equilibrium structure, with high probability, in random games. Our analysis uncovers a sharp geometric dichotomy: non-steep regularizers allow the optimizer to realize the maximal transient surplus via finite-time elimination of suboptimal actions, whereas steep regularizers introduce a vanishing tail correction that can delay surplus saturation. Finally, we discuss whether this leverage persists under bilateral payoff uncertainty and propose a susceptibility measure quantifying which regularizers are most vulnerable to learner-aware strategic steering.

Submission history

From: Yiheng Su [view email]
[v1] Mon, 6 Apr 2026 19:46:45 UTC (59 KB)
[v2] Thu, 21 May 2026 19:10:31 UTC (5,111 KB)

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