In causal inference, estimating heterogeneous treatment effects (HTE) is critical for identifying how different subgroups respond to interventions, with broad applications in fields such as precision medicine and personalized advertising. Although HTE estimation methods aim to improve accuracy, how to provide explicit subgroup descriptions remains unclear, hindering data interpretation and strategic intervention management. In this paper, we propose CURLS, a novel rule learning method leveraging HTE, which can effectively describe subgroups with significant treatment effects. Specifically, we frame causal rule learning as a discrete optimization problem, finely balancing treatment effect with variance and considering the rule interpretability. We design an iterative procedure based on the minorize-maximization algorithm and solve a submodular lower bound as an approximation for the original. Quantitative experiments and qualitative case studies verify that compared with state-of-the-art methods, CURLS can find subgroups where the estimated and true effects are 16.1% and 13.8% higher and the variance is 12.0% smaller, while maintaining similar or better estimation accuracy and rule interpretability. Code is available at https://osf.io/zwp2k/.

An online non-convex optimization problem is considered where the goal is to minimize the flow time (total delay) of a set of jobs by modulating the number of active servers, but with a switching cost associated with changing the number of active servers over time. Each job can be processed by at most one fixed speed server at any time. Compared to the usual online convex optimization (OCO) problem with switching cost, the objective function considered is non-convex and more importantly, at each time, it depends on all past decisions and not just the present one. Both worst-case and stochastic inputs are considered; for both cases, competitive algorithms are derived.

We introduce a new algorithm for solving unconstrained discrete-time optimal control problems. Our method follows a direct multiple shooting approach, and consists of applying the SQP method together with an $\ell_2$ augmented Lagrangian primal-dual merit function. We use the LQR algorithm to efficiently solve the primal-dual Newton-KKT system. As our algorithm is a specialization of NPSQP, it inherits its generic properties, including global convergence, fast local convergence, and the lack of need for second order corrections or dimension expansions, improving on existing direct multiple shooting approaches such as acados, ALTRO, GNMS, FATROP, and FDDP. The solutions of the LQR-shaped subproblems posed by our algorithm can be be parallelized to run in time logarithmic in the number of stages, states, and controls. Moreover, as our method avoids sequential rollouts of the nonlinear dynamics, it can run in $O(1)$ parallel time per line search iteration. Therefore, this paper provides a practical, theoretically sound, and highly parallelizable (for example, with a GPU) method for solving nonlinear discrete-time optimal control problems. An open-source JAX implementation of this algorithm can be found on GitHub (joaospinto/primal_dual_ilqr).

Column selection is an essential tool for structure-preserving low-rank approximation, with wide-ranging applications across many fields, such as data science, machine learning, and theoretical chemistry. In this work, we develop unified methodologies for fast, efficient, and theoretically guaranteed column selection. First we derive and implement a sparsity-exploiting deterministic algorithm applicable to tasks including kernel approximation and CUR decomposition. Next, we develop a matrix-free formalism relying on a randomization scheme satisfying guaranteed concentration bounds, applying this construction both to CUR decomposition and to the approximation of matrix functions of graph Laplacians. Importantly, the randomization is only relevant for the computation of the scores that we use for column selection, not the selection itself given these scores. For both deterministic and matrix-free algorithms, we bound the performance favorably relative to the expected performance of determinantal point process (DPP) sampling and, in select scenarios, that of exactly optimal subset selection. The general case requires new analysis of the DPP expectation. Finally, we demonstrate strong real-world performance of our algorithms on a diverse set of example approximation tasks.

Identifying informative components in binary data is an essential task in many research areas, including life sciences, social sciences, and recommendation systems. Boolean matrix factorization (BMF) is a family of methods that performs this task by efficiently factorizing the data. In real-world settings, the data is often distributed across stakeholders and required to stay private, prohibiting the straightforward application of BMF. To adapt BMF to this context, we approach the problem from a federated-learning perspective, while building on a state-of-the-art continuous binary matrix factorization relaxation to BMF that enables efficient gradient-based optimization. We propose to only share the relaxed component matrices, which are aggregated centrally using a proximal operator that regularizes for binary outcomes. We show the convergence of our federated proximal gradient descent algorithm and provide differential privacy guarantees. Our extensive empirical evaluation demonstrates that our algorithm outperforms, in terms of quality and efficacy, federation schemes of state-of-the-art BMF methods on a diverse set of real-world and synthetic data.

Multi-objective optimization (MOO) is receiving more attention in various fields such as multi-task learning. Recent works provide some effective algorithms with theoretical analysis but they are limited by the standard $L$-smooth or bounded-gradient assumptions, which are typically unsatisfactory for neural networks, such as recurrent neural networks (RNNs) and transformers. In this paper, we study a more general and realistic class of $\ell$-smooth loss functions, where $\ell$ is a general non-decreasing function of gradient norm. We develop two novel single-loop algorithms for $\ell$-smooth MOO problems, Generalized Smooth Multi-objective Gradient descent (GSMGrad) and its stochastic variant, Stochastic Generalized Smooth Multi-objective Gradient descent (SGSMGrad), which approximate the conflict-avoidant (CA) direction that maximizes the minimum improvement among objectives. We provide a comprehensive convergence analysis of both algorithms and show that they converge to an $\epsilon$-accurate Pareto stationary point with a guaranteed $\epsilon$-level average CA distance (i.e., the gap between the updating direction and the CA direction) over all iterations, where totally $\mathcal{O}(\epsilon^{-2})$ and $\mathcal{O}(\epsilon^{-4})$ samples are needed for deterministic and stochastic settings, respectively. Our algorithms can also guarantee a tighter $\epsilon$-level CA distance in each iteration using more samples. Moreover, we propose a practical variant of GSMGrad named GSMGrad-FA using only constant-level time and space, while achieving the same performance guarantee as GSMGrad. Our experiments validate our theory and demonstrate the effectiveness of the proposed methods.

Heterogeneous treatment effect (HTE) estimation from observational data poses significant challenges due to treatment selection bias. Existing methods address this bias by minimizing distribution discrepancies between treatment groups in latent space, focusing on global alignment. However, the fruitful aspect of local proximity, where similar units exhibit similar outcomes, is often overlooked. In this study, we propose Proximity-aware Counterfactual Regression (PCR) to exploit proximity for representation balancing within the HTE estimation context. Specifically, we introduce a local proximity preservation regularizer based on optimal transport to depict the local proximity in discrepancy calculation. Furthermore, to overcome the curse of dimensionality that renders the estimation of discrepancy ineffective--exacerbated by limited data availability for HTE estimation--we develop an informative subspace projector, which trades off minimal distance precision for improved sample complexity. Extensive experiments demonstrate that PCR accurately matches units across different treatment groups, effectively mitigates treatment selection bias, and significantly outperforms competitors. Code is available at https://anonymous.4open.science/status/ncr-B697.

The sample efficiency of Bayesian optimization algorithms depends on carefully crafted acquisition functions (AFs) guiding the sequential collection of function evaluations. The best-performing AF can vary significantly across optimization problems, often requiring ad-hoc and problem-specific choices. This work tackles the challenge of designing novel AFs that perform well across a variety of experimental settings. Based on FunSearch, a recent work using Large Language Models (LLMs) for discovery in mathematical sciences, we propose FunBO, an LLM-based method that can be used to learn new AFs written in computer code by leveraging access to a limited number of evaluations for a set of objective functions. We provide the analytic expression of all discovered AFs and evaluate them on various global optimization benchmarks and hyperparameter optimization tasks. We show how FunBO identifies AFs that generalize well in and out of the training distribution of functions, thus outperforming established general-purpose AFs and achieving competitive performance against AFs that are customized to specific function types and are learned via transfer-learning algorithms.

In this paper we describe a new conceptual framework that connects approximate Dynamic Programming (DP), Model Predictive Control (MPC), and Reinforcement Learning (RL). This framework centers around two algorithms, which are designed largely independently of each other and operate in synergy through the powerful mechanism of Newton's method. We call them the off-line training and the on-line play algorithms. The names are borrowed from some of the major successes of RL involving games; primary examples are the recent (2017) AlphaZero program (which plays chess, [SHS17], [SSS17]), and the similarly structured and earlier (1990s) TD-Gammon program (which plays backgammon, [Tes94], [Tes95], [TeG96]). In these game contexts, the off-line training algorithm is the method used to teach the program how to evaluate positions and to generate good moves at any given position, while the on-line play algorithm is the method used to play in real time against human or computer opponents. Significantly, the synergy between off-line training and on-line play also underlies MPC (as well as other major classes of sequential decision problems), and indeed the MPC design architecture is very similar to the one of AlphaZero and TD-Gammon. This conceptual insight provides a vehicle for bridging the cultural gap between RL and MPC, and sheds new light on some fundamental issues in MPC. These include the enhancement of stability properties through rollout, the treatment of uncertainty through the use of certainty equivalence, the resilience of MPC in adaptive control settings that involve changing system parameters, and the insights provided by the superlinear performance bounds implied by Newton's method.

Black-box optimization (BBO) aims to optimize an objective function by iteratively querying a black-box oracle. This process demands sample-efficient optimization due to the high computational cost of function evaluations. While prior studies focus on forward approaches to learn surrogates for the unknown objective function, they struggle with high-dimensional inputs where valid inputs form a small subspace (e.g., valid protein sequences), which is common in real-world tasks. Recently, diffusion models have demonstrated impressive capability in learning the high-dimensional data manifold. They have shown promising performance in black-box optimization tasks but only in offline settings. In this work, we propose diffusion-based inverse modeling for black-box optimization (Diff-BBO), the first inverse approach leveraging diffusion models for online BBO problem. Diff-BBO distinguishes itself from forward approaches through the design of acquisition function. Instead of proposing candidates in the design space, Diff-BBO employs a novel acquisition function Uncertainty-aware Exploration (UaE) to propose objective function values, which leverages the uncertainty of a conditional diffusion model to generate samples in the design space. Theoretically, we prove that using UaE leads to optimal optimization outcomes. Empirically, we redesign experiments on the Design-Bench benchmark for online settings and show that Diff-BBO achieves state-of-the-art performance.