ICML 2026 论文列表

We study the existence and computation of Nash equilibria in concave games where the players' admissible strategies are subject to shared coupling constraints. Under playerwise concavity of constraints, we prove existence of Nash equilibria. Our proof leverages topological fixed point theory and novel structural insights into the contractibility of feasible sets, and relaxes strong assumptions for existence in prior work. Having established existence, we address the question of whether in the presence of coupling constraints, playerwise independent learning dynamics have convergence guarantees. We address this positively for the class of potential games by designing a convergent algorithm. To account for the possibly nonconvex feasible region, we employ a log barrier regularized gradient ascent with adaptive stepsizes. Starting from an initial feasible strategy profile and under exact gradient feedback, the proposed method converges to an $\epsilon$-approximate constrained Nash equilibrium within $\mathcal{O}(\epsilon^{-3})$ iterations.

Unlearning in diffusion models aims to remove undesirable data or concepts while preserving the utility of pretrained models---two fundamentally conflicting objectives. We propose a principled constrained optimization framework that formulates unlearning as minimizing the deviation from a pretrained model, subject to explicit separation constraints from the unlearning distributions. Specifically, we formulate three constrained optimization problems based on reverse and forward KL divergences, and likelihood constraints. The first two generalize existing approaches for concept and data unlearning, while the third offers a novel and natural formulation for unlearning. Despite the nonconvexity of the KL constraints, we establish strong duality for all three problems, enabling us to explicitly characterize their optimal solutions as unlearning targets and develop primal–dual algorithms for each formulation. Experimental results demonstrate that our KL-constrained approach achieves superior retention-unlearning tradeoffs compared to weight-based baselines for concept and data unlearning, and that our likelihood-based approach matches unlearning effectiveness while better preserving retained concepts compared to baselines.

Capacitated fair-range $k$-clustering generalizes classical $k$-clustering by incorporating both capacity constraints and demographic fairness. In this setting, data points are categorized as clients and facilities; each facility has a capacity and may belong to one or more possibly intersecting demographic groups. The task is to select $k$ facilities as centers and assign each client to a center so that: ($a$) no center exceeds its capacity, ($b$) the number of centers selected from each group lies within specified lower and upper bounds (fair-range constraints), and ($c$) the clustering cost (e.g., $k$-median or $k$-means) is minimized. In a prior work, Thejaswi et al. (2022) showed that even satisfying fair-range constraints is NP-hard, thereby making the problem inapproximable to any polynomial factor. Our first main result strengthens this by showing that inapproximability persists even when the fair-range constraints are trivially satisfiable, highlighting the intrinsic computational complexity of the clustering task itself. These inapproximability results hold even on tree metrics and when the number of groups is logarithmic in the size of the facility set. In light of strong inapproximability results, we focus on a practical setting where the number of groups is constant. Our second main result is a polynomial-time $O(\log k)$- and $O(\log^2 k)$-approximation algorithm for $k$-median and $k$-means objectives, respectively, in this regime. Next, we design constant factor approximation algorithms for these problems that run in fixed parameterized tractable time in $k$. All our approximation guarantees match the best bounds for capacitated clustering without fair-range constraints. Finally, as our third main contribution, we show that our polynomial-time algorithms are, to our knowledge, the first to have provable approximation guarantees that can practically solve problem instances of modest size.

We present a novel framework for embedding hard constraint satisfaction into neural network (NN) architectures, specifically feedforward neural networks and transformers, with input-dependent affine constraints of arbitrary cardinality. Traditional constraint enforcement approaches either rely on penalty-based soft constraints, which offer no guarantee of satisfaction, or on post-processing methods that enforce constraints after the NN is trained, which may lead to suboptimality. We introduce a trainable constraint-affine (CAffine) layer into NNs, yielding CAffNet, which goes beyond enforcing affine constraints via fixed orthogonal or parallel projections and enables joint optimization with network parameters. Moreover, we impose no restrictions on the constraint space dimensions and establish that our construction preserves the universal approximation properties of NNs, while providing provable guarantees on constraint adherence for all inputs. Experimental validation demonstrates robust performance across diverse domains requiring guaranteed constraint satisfaction.