ICML 2025 Papers

Concept Bottleneck Models (CBMs) propose to enhance the trustworthiness of AI systems by constraining their decisions on a set of human understandable concepts. However, CBMs typically rely on datasets with assumedly accurate concept labels—an assumption often violated in practice which we show can significantly degrade performance. To address this, we introduce the Concept Preference Optimization (CPO) objective, a new loss function based on Direct Preference Optimization, which effectively mitigates the negative impact of concept mislabeling on CBM performance. We provide an analysis on some key properties of the CPO objective showing it directly optimizes for the concept’s posterior distribution, and contrast it against Binary Cross Entropy (BCE) where we show CPO is inherently less sensitive to concept noise. We empirically confirm our analysis finding that CPO consistently outperforms BCE in three real-world datasets with and without added label noise

In decision-making problems, the outcome of an intervention often depends on the causal relationships between system components and is highly costly to evaluate. In such settings, causal Bayesian optimization (CBO) exploits the causal relationships between the system variables and sequentially performs interventions to approach the optimum with minimal data. Extending CBO to the multi-outcome setting, we propose *multi-objective Causal Bayesian optimization* (MO-CBO), a paradigm for identifying Pareto-optimal interventions within a known multi-target causal graph. Our methodology first reduces the search space by discarding sub-optimal interventions based on the structure of the given causal graph. We further show that any MO-CBO problem can be decomposed into several traditional multi-objective optimization tasks. Our proposed MO-CBO algorithm is designed to identify Pareto-optimal interventions by iteratively exploring these underlying tasks, guided by relative hypervolume improvement. Experiments on synthetic and real-world causal graphs demonstrate the superiority of our approach over non-causal multi-objective Bayesian optimization in settings where causal information is available.

Existing analysis of Local (Stochastic) Gradient Descent for heterogeneous objectives requires stepsizes $\eta \leq 1/K$ where $K$ is the communication interval, which ensures monotonic decrease of the objective. In contrast, we analyze Local Gradient Descent for logistic regression with separable, heterogeneous data using any stepsize $\eta > 0$. With $R$ communication rounds and $M$ clients, we show convergence at a rate $\mathcal{O}(1/\eta K R)$ after an initial unstable phase lasting for $\widetilde{\mathcal{O}}(\eta K M)$ rounds. This improves upon the existing $\mathcal{O}(1/R)$ rate for general smooth, convex objectives. Our analysis parallels the single machine analysis of Wu et al. (2024) in which instability is caused by extremely large stepsizes, but in our setting another source of instability is large local updates with heterogeneous objectives.

Applications such as engineering design often require us to optimize a black-box function, i.e., a system whose inner processing is not analytically known and whose gradients are not available. Practitioners often have a fixed budget for the number of function evaluations and the performance of an optimization algorithm is measured by its simple regret. In this paper, we study the class of ``Optimistic Optimization'' algorithms for black-box optimization that use a partitioning scheme for the domain. We develop algorithms that learn a good partitioning scheme and use flexible surrogate models such as neural networks in the optimization procedure. For multi-index functions on an $m$-dimensional subspace within $d$ dimensions, our algorithm attains $\tilde{O}(n^{-\beta / d})$ regret, where $\beta = 1 + \frac{d-m}{2m-1}$, as opposed to $\tilde{O}(n^{-1/d})$ for SequOOL, a state-of-the-art optimistic optimization algorithm. Our approach is competitive across a wide range of numerical benchmarks. Additionally, we introduce weight quantization in a large language model as a novel task for black-box optimization. Our approach improves the quality of Activation-aware Weight Quantization (AWQ) of the OPT-1.3B model, achieving an approximate 10\% improvement in performance relative to the best possible unquantized model.

We consider a distributed learning problem, where agents minimize a global objective function by exchanging information over a network. Our approach has two distinct features: (i) It substantially reduces communication by triggering communication only when necessary, and (ii) it is agnostic to the data-distribution among the different agents. We can therefore guarantee convergence even if the local data-distributions of the agents are arbitrarily distinct. We analyze the convergence rate of the algorithm both in convex and nonconvex settings and derive accelerated convergence rates in a convex setting. We also characterize the effect of communication failures and demonstrate that our algorithm is robust to communication failures. The article concludes by presenting numerical results from distributed learning tasks on the MNIST and CIFAR-10 datasets. The experiments underline communication savings of 35\% or more due to the event-based communication strategy, show resilience towards heterogeneous data-distributions, and highlight that our approach outperforms common baselines such as FedAvg, FedProx, SCAFFOLD and FedADMM.

Robustness to outliers is important in machine learning. Many classical problems, including subspace embedding, clustering, and low-rank approximation, lack scalable, outlier-resilient algorithms. This paper considers machine learning problems of the form $\min_{x\in \mathbb{R}^d} F(x)$, where $F(x)=\sum_{i=1}^n F_i(x)$, and their robust counterparts $\min_{x\in\mathbb{R}^d} F^{(m)}(x)$, where $F^{(m)}(x)$ denotes the sum of all but the $m$ largest $F_i(x)$ values. We develop a general framework for constructing $\epsilon$-coresets for such robust problems, where an $\epsilon$-coreset is a weighted subset of functions $\{F_1(x),\dots,F_n(x)\}$ that provides a $(1+\epsilon)$-approximation to $F(x)$. Specifically, if the original problem $F$ has total sensitivity $T$ and admits a vanilla $\epsilon$-coreset of size $S$, our algorithm constructs an $\epsilon$-coreset of size $\tilde{O}(\frac{mT}{\epsilon})+S$ for the robust objective $F^{(m)}$. This coreset size can be shown to be near-tight for $\ell_2$ subspace embedding. Our coreset algorithm has scalable running time and leads to new or improved algorithms for the robust optimization problems. Empirical evaluations demonstrate that our coresets outperform uniform sampling on real-world data sets.

Understanding generalization of overparametrized models remains a fundamental challenge in machine learning. The literature mostly studies generalization from an interpolation point of view, taking convergence towards a global minimum of the training loss for granted. This interpolation paradigm does not seem valid for complex tasks such as in-context learning or diffusion. It has instead been empirically observed that the trained models go from global minima to spurious local minima of the training loss as the number of training samples becomes larger than some level we call optimization threshold. This paper explores theoretically this phenomenon in the context of two-layer ReLU networks. We demonstrate that, despite overparametrization, networks might converge towards simpler solutions rather than interpolating training data, which leads to a drastic improvement on the test loss. Our analysis relies on the so called early alignment phase, during which neurons align toward specific directions. This directional alignment leads to a simplicity bias, wherein the network approximates the ground truth model without converging to the global minimum of the training loss. Our results suggest this bias, resulting in an optimization threshold from which interpolation is not reached anymore, is beneficial and enhances the generalization of trained models.

Decision-makers often adaptively influence downstream competitive agents' behavior to minimize their cost, yet in doing so face critical challenges: $(i)$ decision-makers might not *a priori* know the agents' objectives; $(ii)$ agents might *learn* their responses, introducing stochasticity and non-stationarity into the decision-making process; and $(iii)$ there may be additional non-strategic environmental stochasticity. Characterizing convergence of this complex system is contingent on how the decision-maker controls for the tradeoff between the induced drift and additional noise from the learning agent behavior and environmental stochasticity. To understand how the learning agents' behavior is influenced by the decision-maker’s actions, we first consider a decision-maker that deploys an arbitrary sequence of actions which induces a sequence of games and corresponding equilibria. We characterize how the drift and noise in the agents' stochastic algorithms decouples from their optimization error. Leveraging this decoupling and accompanying finite-time efficiency estimates, we design decision-maker algorithms that control the induced drift relative to the agent noise. This enables efficient finite-time tracking of game theoretic equilibrium concepts that adhere to the incentives of the players' collective learning processes.

Shuffling-type gradient methods are favored in practice for their simplicity and rapid empirical performance. Despite extensive development of convergence guarantees under various assumptions in recent years, most require the Lipschitz smoothness condition, which is often not met in common machine learning models. We highlight this issue with specific counterexamples. To address this gap, we revisit the convergence rates of shuffling-type gradient methods without assuming Lipschitz smoothness. Using our stepsize strategy, the shuffling-type gradient algorithm not only converges under weaker assumptions but also match the current best-known convergence rates, thereby broadening its applicability. We prove the convergence rates for nonconvex, strongly convex, and non-strongly convex cases, each under both random reshuffling and arbitrary shuffling schemes, under a general bounded variance condition. Numerical experiments further validate the performance of our shuffling-type gradient algorithm, underscoring its practical efficacy.

Behavior regularization, which constrains the policy to stay close to some behavior policy, is widely used in offline reinforcement learning (RL) to manage the risk of hazardous exploitation of unseen actions. Nevertheless, existing literature on behavior-regularized RL primarily focuses on explicit policy parameterizations, such as Gaussian policies. Consequently, it remains unclear how to extend this framework to more advanced policy parameterizations, such as diffusion models. In this paper, we introduce BDPO, a principled behavior-regularized RL framework tailored for diffusion-based policies, thereby combining the expressive power of diffusion policies and the robustness provided by regularization. The key ingredient of our method is to calculate the Kullback-Leibler (KL) regularization analytically as the accumulated discrepancies in reverse-time transition kernels along the diffusion trajectory. By integrating the regularization, we develop an efficient two-time-scale actor-critic RL algorithm that produces the optimal policy while respecting the behavior constraint. Comprehensive evaluations conducted on synthetic 2D tasks and continuous control tasks from the D4RL benchmark validate its effectiveness and superior performance.

Tensors play a crucial role in numerous scientific and engineering fields. This paper addresses the low-multilinear-rank tensor completion problem, a fundamental task in tensor-related applications. By exploiting the manifold structure inherent to the fixed-multilinear-rank tensor set, we introduce a simple yet highly effective preconditioned Riemannian metric and propose the Preconditioned Riemannian Gradient Descent (PRGD) algorithm. Compared to the standard Riemannian Gradient Descent (RGD), PRGD achieves faster convergence while maintaining the same order of per-iteration computational complexity. Theoretically, we provide the recovery guarantee for PRGD under near-optimal sampling complexity. Numerical results highlight the efficiency of PRGD, outperforming state-of-the-art methods on both synthetic data and real-world video inpainting tasks.

Bilevel optimization is a powerful tool for many machine learning problems, such as hyperparameter optimization and meta-learning. Estimating hypergradients (also known as implicit gradients) is crucial for developing gradient-based methods for bilevel optimization. In this work, we propose a computationally efficient technique for incorporating curvature information into the approximation of hypergradients and present a novel algorithmic framework based on the resulting enhanced hypergradient computation. We provide convergence rate guarantees for the proposed framework in both deterministic and stochastic scenarios, particularly showing improved computational complexity over popular gradient-based methods in the deterministic setting. This improvement in complexity arises from a careful exploitation of the hypergradient structure and the inexact Newton method. In addition to the theoretical speedup, numerical experiments demonstrate the significant practical performance benefits of incorporating curvature information.

We introduce Wasserstein Policy Optimization (WPO), an actor-critic algorithm for reinforcement learning in continuous action spaces. WPO can be derived as an approximation to Wasserstein gradient flow over the space of all policies projected into a finite-dimensional parameter space (e.g., the weights of a neural network), leading to a simple and completely general closed-form update. The resulting algorithm combines many properties of deterministic and classic policy gradient methods. Like deterministic policy gradients, it exploits knowledge of the *gradient* of the action-value function with respect to the action. Like classic policy gradients, it can be applied to stochastic policies with arbitrary distributions over actions -- without using the reparameterization trick. We show results on the DeepMind Control Suite and a magnetic confinement fusion task which compare favorably with state-of-the-art continuous control methods.

We study the classical optimization problem $\min_{x \in \mathbb{R}^d} f(x)$ and analyze the gradient descent (GD) method in both nonconvex and convex settings. It is well-known that, under the $L$–smoothness assumption ($\|\| \nabla^2 f(x) \|\| \leq L$), the optimal point minimizing the quadratic upper bound $f(x_k) + \langle \nabla f(x_k), x_{k+1} - x_k \rangle + \frac{L}{2} \|\| x_{k+1} - x_k \|\|^2$ is $x_{k+1} = x_k - \gamma_k \nabla f(x_k)$ with step size $\gamma_k = \frac{1}{L}$. Surprisingly, a similar result can be derived under the $\ell$-generalized smoothness assumption ($\|\| \nabla^2 f(x) \|\| \leq \ell( \|\| \nabla f(x) \|\| )$). In this case, we derive the step size $$\gamma_k = \int_{0}^{1} \frac{d v}{\ell( \|\| \nabla f(x_k) \|\| + \|\| \nabla f(x_k) \|\| v)}.$$ Using this step size rule, we improve upon existing theoretical convergence rates and obtain new results in several previously unexplored setups.

Neural Operators that directly learn mappings between function spaces, such as Deep Operator Networks (DONs) and Fourier Neural Operators (FNOs), have received considerable attention. Despite the universal approximation guarantees for DONs and FNOs, there is currently no optimization convergence guarantee for learning such networks using gradient descent (GD). In this paper, we address this open problem by presenting a unified framework for optimization based on GD and applying it to establish convergence guarantees for both DONs and FNOs. In particular, we show that the losses associated with both of these neural operators satisfy two conditions—restricted strong convexity (RSC) and smoothness—that guarantee a decrease on their loss values due to GD. Remarkably, these two conditions are satisfied for each neural operator due to different reasons associated with the architectural differences of the respective models. One takeaway that emerges from the theory is that wider networks benefit optimization convergence guarantees for both DONs and FNOs. We present empirical results on canonical operator learning problems to support our theoretical results and find that larger widths benefit training.

We present several advances on neural operators by viewing the action of operator layers as the minimizers of Bregman regularized optimization problems over Banach function spaces. The proposed framework allows interpreting the activation operators as Bregman proximity operators from dual to primal space. This novel viewpoint is general enough to recover classical neural operators as well as a new variant, coined Bregman neural operators, which includes the inverse activation operator and features the same expressivity of standard neural operators. Numerical experiments support the added benefits of the Bregman variant of Fourier neural operators for training deeper and more accurate models.

We study inverse optimization (IO), where the goal is to use a parametric optimization program as the hypothesis class to infer relationships between input-decision pairs. Most of the literature focuses on learning only the objective function, as learning the constraint function (i.e., feasible regions) leads to nonconvex training programs. Motivated by this, we focus on learning feasible regions for known linear objectives, and introduce two training losses along with a hypothesis class to parameterize the constraint function. Our hypothesis class surpasses the previous objective-only method by naturally capturing discontinuous behaviors in input-decision pairs. We introduce a customized block coordinate descent algorithm with a smoothing technique to solve the training problems, while for further restricted hypothesis classes, we reformulate the training optimization as a tractable convex program or mixed integer linear program. Synthetic experiments and two power system applications including comparisons with state-of-the-art approaches showcase and validate the proposed approach.

We analyze nonlinearly preconditioned gradient methods for solving smooth minimization problems. We introduce a generalized smoothness property, based on the notion of abstract convexity, that is broader than Lipschitz smoothness and provide sufficient first- and second-order conditions. Notably, our framework encapsulates algorithms associated with the gradient clipping method and brings out novel insights for the class of $(L_0,L_1)$-smooth functions that has received widespread interest recently, thus allowing us to extend beyond already established methods. We investigate the convergence of the proposed method in both the convex and nonconvex setting.

In the field of machine learning (ML), an essential type of decision-related problem is known as AUF (Avoiding Undesired Future): if an ML model predicts an undesired outcome, how can decisions be made to prevent it? Recently, a novel framework called *rehearsal learning* has been proposed to address the AUF problem. Despite its utility in modeling uncertainty for decision-making, it remains unclear *under what conditions* and *how* optimal actions that maximize the *AUF probability* can be identified. In this paper, we propose *CARE* (CAnonical REctangle), a condition under which the maximum AUF probability can be achieved. Under the CARE condition, we present a projection-Newton algorithm to select actions and prove that the algorithm achieves superlinear convergence to the optimal one. Besides, we provide a generalization method for adopting the algorithm to AUF scenarios beyond the CARE condition. Finally, we demonstrate that a closed-form solution exists when the outcome is a singleton variable, substantially reducing the time complexity of decision-making. Experiments validate the effectiveness and efficiency of our method.