This work considers the problem of sampling from a probability distribution known up to a normalization constant while satisfying a set of statistical constraints specified by the expected values of general nonlinear functions. This problem finds applications in, e.g., Bayesian inference, where it can constrain moments to evaluate counterfactual scenarios or enforce desiderata such as prediction fairness. Methods developed to handle support constraints, such as those based on mirror maps, barriers, and penalties, are not suited for this task. This work therefore relies on gradient descent-ascent dynamics in Wasserstein space to put forward a discretetime primal-dual Langevin Monte Carlo algorithm (PD-LMC) that simultaneously constrains the target distribution and samples from it. We analyze the convergence of PD-LMC under standard assumptions on the target distribution and constraints, namely (strong) convexity and log-Sobolev inequalities. To do so, we bring classical optimization arguments for saddle-point algorithms to the geometry of Wasserstein space. We illustrate the relevance and effectiveness of PD-LMC in several applications.

A.1 Implementation Details There are mainly three parameters in the selective search approach: scale, σ and min_size. The parameter scale controls the number and size of the produced segments, that higher scale means less but larger segments. The parameter σ is the diameter of the Gaussian kernel used for smoothing the image prior for segmentation. We use the default values of this approach: scale = 500, σ = 0.9 and min_size = 10. A.2 Visualization Figure 1 shows the proposals generated by the selective search approach, which shows reasonably good to cover the objects.

We focus on generative AI for a type of data that still represent one of the most prevalent form of data: tabular data. Our paper introduces two key contributions: a new powerful class of forest-based models fit for such tasks and a simple training algorithm with strong convergence guarantees in a boosting model that parallels that of the original weak / strong supervised learning setting. This algorithm can be implemented by a few tweaks to the most popular induction scheme for decision tree induction (i.e.

Most existing geometry processing algorithms use meshes as the default shape representation. Manipulating meshes, however, requires one to maintain high quality in the surface discretization. For example, changing the topology of a mesh usually requires additional procedures such as remeshing. This paper instead proposes the use of neural fields for geometry processing. Neural fields can compactly store complicated shapes without spatial discretization. Moreover, neural fields are infinitely differentiable, which allows them to be optimized for objectives that involve higher-order derivatives.

AI's energy use already represents as much as 20 percent of global data-center power demand, research published Thursday in the journal Joule shows. That demand from AI, the research states, could double by the end of this year, comprising nearly half of all total data-center electricity consumption worldwide, excluding the electricity used for bitcoin mining. The new research is published in a commentary by Alex de Vries-Gao, the founder of Digiconomist, a research company that evaluates the environmental impact of technology. De Vries-Gao started Digiconomist in the late 2010s to explore the impact of bitcoin mining, another extremely energy-intensive activity, would have on the environment. Looking at AI, he says, has grown more urgent over the past few years because of the widespread adoption of ChatGPT and other large language models that use massive amounts of energy. According to his research, worldwide AI energy demand is now set to surpass demand from bitcoin mining by the end of this year.

Artificial intelligence systems could account for nearly half of datacentre power consumption by the end of this year, analysis has revealed. The estimates by Alex de Vries-Gao, the founder of the Digiconomist tech sustainability website, came as the International Energy Agency forecast that AI would require almost as much energy by the end of this decade as Japan uses today. De Vries-Gao's calculations, to be published in the sustainable energy journal Joule, are based on the power consumed by chips made by Nvidia and Advanced Micro Devices that are used to train and operate AI models. The paper also takes into account the energy consumption of chips used by other companies, such as Broadcom. The IEA estimates that all data centres – excluding mining for cryptocurrencies – consumed 415 terawatt hours (TWh) of electricity last year.

Prediction+optimization is a common real-world paradigm where we have to predict problem parameters before solving the optimization problem. However, the criteria by which the prediction model is trained are often inconsistent with the goal of the downstream optimization problem. Recently, decision-focused prediction approaches, such as SPO+ and direct optimization, have been proposed to fill this gap. However, they cannot directly handle the soft constraints with the max operator required in many real-world objectives. This paper proposes a novel analytically differentiable surrogate objective framework for real-world linear and semi-definite negative quadratic programming problems with soft linear and non-negative hard constraints. This framework gives the theoretical bounds on constraints' multipliers, and derives the closed-form solution with respect to predictive parameters and thus gradients for any variable in the problem. We evaluate our method in three applications extended with soft constraints: synthetic linear programming, portfolio optimization, and resource provisioning, demonstrating that our method outperforms traditional two-staged methods and other decision-focused approaches.

The Bayes-Adaptive Markov Decision Process (BAMDP) formalism pursues the Bayes-optimal solution to the exploration-exploitation trade-off in reinforcement learning. As the computation of exact solutions to Bayesian reinforcement-learning problems is intractable, much of the literature has focused on developing suitable approximation algorithms. In this work, before diving into algorithm design, we first define, under mild structural assumptions, a complexity measure for BAMDP planning. As efficient exploration in BAMDPs hinges upon the judicious acquisition of information, our complexity measure highlights the worst-case difficulty of gathering information and exhausting epistemic uncertainty. To illustrate its significance, we establish a computationally-intractable, exact planning algorithm that takes advantage of this measure to show more efficient planning. We then conclude by introducing a specific form of state abstraction with the potential to reduce BAMDP complexity and gives rise to a computationally-tractable, approximate planning algorithm.