Stochastic optimization algorithms are widely used for large-scale data analysis due to their low per-iteration costs, but they often suffer from slow asymptotic convergence caused by inherent variance. Variance-reduced techniques have been therefore used to address this issue in structured sparse models utilizing sparsity-inducing norms or $\ell_0$-norms. However, these techniques are not directly applicable to complex (non-convex) graph sparsity models, which are essential in applications like disease outbreak monitoring and social network analysis. In this paper, we introduce two stochastic variance-reduced gradient-based methods to solve graph sparsity optimization: GraphSVRG-IHT and GraphSCSG-IHT. We provide a general framework for theoretical analysis, demonstrating that our methods enjoy a linear convergence speed. Extensive experiments validate

In this article, we focus on solving a class of distributed optimization problems involving $n$ agents with the local objective function at every agent $i$ given by the difference of two convex functions $f_i$ and $g_i$ (difference-of-convex (DC) form), where $f_i$ and $g_i$ are potentially nonsmooth. The agents communicate via a directed graph containing $n$ nodes. We create smooth approximations of the functions $f_i$ and $g_i$ and develop a distributed algorithm utilizing the gradients of the smooth surrogates and a finite-time approximate consensus protocol. We term this algorithm as DDC-Consensus. The developed DDC-Consensus algorithm allows for non-symmetric directed graph topologies and can be synthesized distributively. We establish that the DDC-Consensus algorithm converges to a stationary point of the nonconvex distributed optimization problem. The performance of the DDC-Consensus algorithm is evaluated via a simulation study to solve a nonconvex DC-regularized distributed least squares problem. The numerical results corroborate the efficacy of the proposed algorithm.

This paper proposes a fully data-driven approach for optimal control of nonlinear control-affine systems represented by a stochastic diffusion. The focus is on the scenario where both the nonlinear dynamics and stage cost functions are unknown, while only control penalty function and constraints are provided. Leveraging the theory of reproducing kernel Hilbert spaces, we introduce novel kernel mean embeddings (KMEs) to identify the Markov transition operators associated with controlled diffusion processes. The KME learning approach seamlessly integrates with modern convex operator-theoretic Hamilton-Jacobi-Bellman recursions. Thus, unlike traditional dynamic programming methods, our approach exploits the ``kernel trick'' to break the curse of dimensionality. We demonstrate the effectiveness of our method through numerical examples, highlighting its ability to solve a large class of nonlinear optimal control problems.

Many roboticists dream of presenting a robot with a task in the evening and returning the next morning to find the robot capable of solving the task. What is preventing us from achieving this? Sim-to-real reinforcement learning (RL) has achieved impressive performance on challenging robotics tasks, but requires substantial human effort to set up the task in a way that is amenable to RL. It's our position that algorithmic improvements in policy optimization and other ideas should be guided towards resolving the primary bottleneck of shaping the training environment, i.e., designing observations, actions, rewards and simulation dynamics. Most practitioners don't tune the RL algorithm, but other environment parameters to obtain a desirable controller. We posit that scaling RL to diverse robotic tasks will only be achieved if the community focuses on automating environment shaping procedures.

Contact-implicit trajectory optimization (CITO) is an effective method to plan complex trajectories for various contact-rich systems including manipulation and locomotion. CITO formulates a mathematical program with complementarity constraints (MPCC) that enforces that contact forces must be zero when points are not in contact. However, MPCC solve times increase steeply with the number of allowable points of contact, which limits CITO's applicability to problems in which only a few, simple geometries are allowed to make contact. This paper introduces simultaneous trajectory optimization and contact selection (STOCS), as an extension of CITO that overcomes this limitation. The innovation of STOCS is to identify salient contact points and times inside the iterative trajectory optimization process. This effectively reduces the number of variables and constraints in each MPCC invocation. The STOCS framework, instantiated with key contact identification subroutines, renders the optimization of manipulation trajectories computationally tractable even for high-fidelity geometries consisting of tens of thousands of vertices.

Explanation regularisation (ER) has been introduced as a way to guide models to make their predictions in a manner more akin to humans, i.e., making their attributions "plausible". This is achieved by introducing an auxiliary explanation loss, that measures how well the output of an input attribution technique for the model agrees with relevant human-annotated rationales. One positive outcome of using ER appears to be improved performance in out-of-domain (OOD) settings, presumably due to an increased reliance on "plausible" tokens. However, previous work has under-explored the impact of the ER objective on model attributions, in particular when obtained with techniques other than the one used to train ER. In this work, we contribute a study of ER's effectiveness at informing classification decisions on plausible tokens, and the relationship between increased plausibility and robustness to OOD conditions. Through a series of analyses, we find that the connection between ER and the ability of a classifier to rely on plausible features has been overstated and that a stronger reliance on plausible tokens does not seem to be the cause for any perceived OOD improvements.

Identifying high-revenue mechanisms that are both dominant strategy incentive compatible (DSIC) and individually rational (IR) is a fundamental challenge in auction design. While theoretical approaches have encountered bottlenecks in multi-item auctions, there has been much empirical progress in automated designing such mechanisms using machine learning. However, existing research primarily focuses on randomized auctions, with less attention given to the more practical deterministic auctions. Therefore, this paper investigates the automated design of deterministic auctions and introduces OD-VVCA, an objective decomposition approach for automated designing Virtual Valuations Combinatorial Auctions (VVCAs). Firstly, we restrict our mechanism to deterministic VVCAs, which are inherently DSIC and IR. Afterward, we utilize a parallelizable dynamic programming algorithm to compute the allocation and revenue outcomes of a VVCA efficiently. We then decompose the revenue objective function into continuous and piecewise constant discontinuous components, optimizing each using distinct methods. Extensive experiments show that OD-VVCA achieves high revenue in multi-item auctions, especially in large-scale settings where it outperforms both randomized and deterministic baselines, indicating its efficacy and scalability.

Personalized Federated Learning (PFL) is a commonly used framework that allows clients to collaboratively train their personalized models. PFL is particularly useful for handling situations where data from different clients are not independent and identically distributed (non-IID). Previous research in PFL implicitly assumes that clients can gain more benefits from those with similar data distributions. Correspondingly, methods such as personalized weight aggregation are developed to assign higher weights to similar clients during training. We pose a question: can a client benefit from other clients with dissimilar data distributions and if so, how? This question is particularly relevant in scenarios with a high degree of non-IID, where clients have widely different data distributions, and learning from only similar clients will lose knowledge from many other clients. We note that when dealing with clients with similar data distributions, methods such as personalized weight aggregation tend to enforce their models to be close in the parameter space. It is reasonable to conjecture that a client can benefit from dissimilar clients if we allow their models to depart from each other. Based on this idea, we propose DiversiFed which allows each client to learn from clients with diversified data distribution in personalized federated learning. DiversiFed pushes personalized models of clients with dissimilar data distributions apart in the parameter space while pulling together those with similar distributions. In addition, to achieve the above effect without using prior knowledge of data distribution, we design a loss function that leverages the model similarity to determine the degree of attraction and repulsion between any two models. Experiments on several datasets show that DiversiFed can benefit from dissimilar clients and thus outperform the state-of-the-art methods.

This paper is concerned with personalized pricing models aimed at maximizing the expected revenues or profits for a single item. While it is essential for personalized pricing to predict the purchase probabilities for each consumer, these predicted values are inherently subject to unavoidable errors that can negatively impact the realized revenues and profits. To address this issue, we focus on robust optimization techniques that yield reliable solutions to optimization problems under uncertainty. Specifically, we propose a robust optimization model for personalized pricing that accounts for the uncertainty of predicted purchase probabilities. This model can be formulated as a mixed-integer linear optimization problem, which can be solved exactly using mathematical optimization solvers. We also develop a Lagrangian decomposition algorithm combined with line search to efficiently find high-quality solutions for large-scale optimization problems. Experimental results demonstrate the effectiveness of our robust optimization model and highlight the utility of our Lagrangian decomposition algorithm in terms of both computational efficiency and solution quality.

This technical report investigates variants of the Latent Inceptionism on Molecules (LIMO) framework to improve the properties of generated molecules. We conduct ablative studies of molecular representation, decoder model, and surrogate model training scheme. The experiments suggest that an autogressive Transformer decoder with GroupSELFIES achieves the best average properties for the random generation task. LIMO (Eckmann et al. (2022)) is a molecular generation technique that improves a given set of properties by mapping molecules to a latent space and uses inexpensive property surrogates to turn a discrete space optimization problem into a continuous one. There are multiple components to this framework which are described below.