No Coin Left Behind: Maximizing Strategic Surplus Against No-Regret Dynamics
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| author | Su, Yiheng Vlatakis-Gkaragkounis, Emmanouil-Vasileios |
| author_facet | Su, Yiheng Vlatakis-Gkaragkounis, Emmanouil-Vasileios |
| contents | 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 $Ω(ηT/\mathrm{poly}(n,m))$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_05129 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | No Coin Left Behind: Maximizing Strategic Surplus Against No-Regret Dynamics Su, Yiheng Vlatakis-Gkaragkounis, Emmanouil-Vasileios Computer Science and Game Theory Machine Learning 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 $Ω(ηT/\mathrm{poly}(n,m))$ 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. |
| title | No Coin Left Behind: Maximizing Strategic Surplus Against No-Regret Dynamics |
| topic | Computer Science and Game Theory Machine Learning |
| url | https://arxiv.org/abs/2604.05129 |