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Robust equilibria in continuous games: From strategic to dynamic robustness
Kyriakos Lotidis, Panayotis Mertikopoulos, Nicholas Bambos, Jose Blanchet
https://arxiv.org/abs/2512.08138 https://arxiv.org/pdf/2512.08138 https://arxiv.org/html/2512.08138
arXiv:2512.08138v1 Announce Type: new
Abstract: In this paper, we examine the robustness of Nash equilibria in continuous games, under both strategic and dynamic uncertainty. Starting with the former, we introduce the notion of a robust equilibrium as those equilibria that remain invariant to small -- but otherwise arbitrary -- perturbations to the game's payoff structure, and we provide a crisp geometric characterization thereof. Subsequently, we turn to the question of dynamic robustness, and we examine which equilibria may arise as stable limit points of the dynamics of "follow the regularized leader" (FTRL) in the presence of randomness and uncertainty. Despite their very distinct origins, we establish a structural correspondence between these two notions of robustness: strategic robustness implies dynamic robustness, and, conversely, the requirement of strategic robustness cannot be relaxed if dynamic robustness is to be maintained. Finally, we examine the rate of convergence to robust equilibria as a function of the underlying regularizer, and we show that entropically regularized learning converges at a geometric rate in games with affinely constrained action spaces.
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Verification of Sequential Convex Programming for Parametric Non-convex Optimization
Rajiv Sambharya, Nikolai Matni, George Pappas
https://arxiv.org/abs/2511.10622 https://arxiv.org/pdf/2511.10622 https://arxiv.org/html/2511.10622
arXiv:2511.10622v1 Announce Type: new
Abstract: We introduce a verification framework to exactly verify the worst-case performance of sequential convex programming (SCP) algorithms for parametric non-convex optimization. The verification problem is formulated as an optimization problem that maximizes a performance metric (e.g., the suboptimality after a given number of iterations) over parameters constrained to be in a parameter set and iterate sequences consistent with the SCP update rules. Our framework is general, extending the notion of SCP to include both conventional variants such as trust-region, convex-concave, and prox-linear methods, and algorithms that combine convex subproblems with rounding steps, as in relaxing and rounding schemes. Unlike existing analyses that may only provide local guarantees under limited conditions, our framework delivers global worst-case guarantees--quantifying how well an SCP algorithm performs across all problem instances in the specified family. Applications in control, signal processing, and operations research demonstrate that our framework provides, for the first time, global worst-case guarantees for SCP algorithms in the parametric setting.
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Time-periodic branched transport
Jun Kitagawa, Cecilia Mikat
https://arxiv.org/abs/2511.10498 https://arxiv.org/pdf/2511.10498 https://arxiv.org/html/2511.10498
arXiv:2511.10498v1 Announce Type: new
Abstract: We develop a new framework for branched transport between probability measures which are allowed to vary in time. This framework can be used to model problems where the underlying transportation network displays a branched structure, but the source and target mass distributions can change cyclically over time, such as road networks or circulatory systems. We introduce the notion of time-dependent transport paths along with associated energies and distances, and prove existence of transport paths whose energy achieves the distance. We also show the time-dependent transport yields a metric structure on subsets of appropriately defined measure-valued Sobolev spaces.
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Residual Symmetry Reductions and Painlev\'e Solitons
Yan Li, Ya-Rong Xia, Ruo-Xia Yao, S. Y. Lou
https://arxiv.org/abs/2511.09077 https://arxiv.org/pdf/2511.09077 https://arxiv.org/html/2511.09077
arXiv:2511.09077v1 Announce Type: new
Abstract: This letter introduces the novel concept of Painlev\'e solitons -- waves arising from the interaction between Painlev\'e waves and solitons in integrable systems. Painlev\'e solitons may also be viewed as solitons propagating against a Painlev\'e wave background, in analogy with the established notion of elliptic solitons, which refer to solitons on an elliptic wave background. By employing a novel symmetry decomposition method aided by nonlocal residual symmetries, we explicitly construct (extended) Painlev\'e II solitons for the Korteweg-de Vries (KdV) equation and (extended) Painlev\'e IV solitons for the Boussinesq equation.
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Robust forecast aggregation via additional queries
Rafael Frongillo, Mary Monroe, Eric Neyman, Bo Waggoner
https://arxiv.org/abs/2512.05271 https://arxiv.org/pdf/2512.05271 https://arxiv.org/html/2512.05271
arXiv:2512.05271v1 Announce Type: new
Abstract: We study the problem of robust forecast aggregation: combining expert forecasts with provable accuracy guarantees compared to the best possible aggregation of the underlying information. Prior work shows strong impossibility results, e.g. that even under natural assumptions, no aggregation of the experts' individual forecasts can outperform simply following a random expert (Neyman and Roughgarden, 2022).
In this paper, we introduce a more general framework that allows the principal to elicit richer information from experts through structured queries. Our framework ensures that experts will truthfully report their underlying beliefs, and also enables us to define notions of complexity over the difficulty of asking these queries. Under a general model of independent but overlapping expert signals, we show that optimal aggregation is achievable in the worst case with each complexity measure bounded above by the number of agents $n$. We further establish tight tradeoffs between accuracy and query complexity: aggregation error decreases linearly with the number of queries, and vanishes when the "order of reasoning" and number of agents relevant to a query is $\omega(\sqrt{n})$. These results demonstrate that modest extensions to the space of expert queries dramatically strengthen the power of robust forecast aggregation. We therefore expect that our new query framework will open up a fruitful line of research in this area.
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