No Coin Left Behind: Maximizing Strategic Surplus Against No-Regret Dynamics
We investigate the strategic surplus obtainable against a Follow-the-Regularized-Leader (FTRL) learner with constant step size $η$ 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 $Ω(N_{\mathrm{sub}}/η)$, 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 $Ω(ηT/\mat...
| Authors | Yiheng Su, Emmanouil-Vasileios Vlatakis-Gkaragkounis |
|---|---|
| Primary category | cs.GT |
| Published | 6 April 2026 |
| Last updated at source | 21 May 2026 |
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