We consider the decentralized stochastic asynchronous optimization setup, where many workers asynchronously calculate stochastic gradients and asynchronously communicate with each other using edges in a multigraph. For both homogeneous and heterogeneous setups, we prove new time complexity lower bounds under the assumption that computation and communication speeds are bounded.

We study sequential general online regression, known also as sequential probability assignments, under logarithmic loss when compared against a broad class of experts. We obtain tight, often matching, lower and upper bounds for sequential minimax regret, which is defined as the excess loss incurred by the predictor over the best expert in the class. After proving a general upper bound we consider some specific classes of experts from Lipschitz class to bounded Hessian class and derive matching lower and upper bounds with provably optimal constants. Our bounds work for a wide range of values of the data dimension and the number of rounds. To derive lower bounds, we use tools from information theory (e.g., Shtarkov sum), and for upper bounds we resort to new "smooth truncated covering" of the class of experts. This allows us to find constructive proofs by applying a simple and novel truncated Bayesian algorithm. Our proofs are substantially simpler than the existing ones and yet provide tighter (and often optimal) bounds.

We study sequential general online regression, known also as sequential probability assignments, under logarithmic loss when compared against a broad class of experts. We obtain tight, often matching, lower and upper bounds for sequential minimax regret, which is defined as the excess loss incurred by the predictor over the best expert in the class. After proving a general upper bound we consider some specific classes of experts from Lipschitz class to bounded Hessian class and derive matching lower and upper bounds with provably optimal constants. Our bounds work for a wide range of values of the data dimension and the number of rounds. To derive lower bounds, we use tools from information theory (e.g., Shtarkov sum), and for upper bounds we resort to new "smooth truncated covering" of the class of experts. This allows us to find constructive proofs by applying a simple and novel truncated Bayesian algorithm. Our proofs are substantially simpler than the existing ones and yet provide tighter (and often optimal) bounds.

During a press conference with Japans Prime Minister Shigeru Ishiba, President Trump said relations with North Korea will happen. North Korean dictator Kim Jong Un has overseen tests of newly developed AI-powered suicide drones and called for their increased production, North Korean state media said Thursday. Photos released from the communist country show Kim inspecting new upgraded reconnaissance drones that are capable of detecting various tactical targets and enemy activities on land and at sea, KCNA state news agency said. Kim said unmanned control and AI capability must be the top priorities in modern arms development. North Korean leader Kim Jong Un has overseen tests of newly developed AI-powered suicide drones and called for their increased production, North Korean state media said.

Radiation therapy, treating over half of all cancer patients, involves using specialized machines to direct high-energy beams at tumors, aiming to damage cancer cells while minimizing harm to nearby healthy tissues. Customizing the shape and intensity of radiation beams for each patient leads to solving large-scale constrained optimization problems that need to be solved within tight clinical time-frame. At the core of these challenges is a large matrix that is commonly sparsified for computational efficiency by neglecting small elements. Such a crude approximation can degrade the quality of treatment, potentially causing unnecessary radiation exposure to healthy tissues--this may lead to significant radiation-induced side effects--or delivering inadequate radiation to the tumor, which is crucial for effective tumor treatment. In this work, we demonstrate, for the first time, that randomized sketch tools can effectively sparsify this matrix without sacrificing treatment quality. We also develop a novel randomized sketch method with desirable theoretical guarantees that outperforms existing techniques in practical application. Beyond developing a novel randomized sketch method, this work emphasizes the potential of harnessing scientific computing tools, crucial in today's big data analysis, to tackle computationally intensive challenges in healthcare. The application of these tools could have a profound impact on the lives of numerous cancer patients.

Energy-based models are a simple yet powerful class of probabilistic models, but their widespread adoption has been limited by the computational burden of training them. We propose a novel loss function called Energy Discrepancy (ED) which does not rely on the computation of scores or expensive Markov chain Monte Carlo. We show that energy discrepancy approaches the explicit score matching and negative log-likelihood loss under different limits, effectively interpolating between both. Consequently, minimum energy discrepancy estimation overcomes the problem of nearsightedness encountered in score-based estimation methods, while also enjoying theoretical guarantees. Through numerical experiments, we demonstrate that ED learns low-dimensional data distributions faster and more accurately than explicit score matching or contrastive divergence. For high-dimensional image data, we describe how the manifold hypothesis puts limitations on our approach and demonstrate the effectiveness of energy discrepancy by training the energy-based model as a prior of a variational decoder model.