Related papers: On the Properties of the Softmax Function with App…
This paper considers convex games involving multiple agents that aim to minimize their own cost functions using locally available information. A common assumption in the study of such games is that the agents are symmetric, meaning that…
Metric learning aims at learning a distance which is consistent with the semantic meaning of the samples. The problem is generally solved by learning an embedding for each sample such that the embeddings of samples of the same category are…
We simplify the proof of some widely used theoretical theorems, extending their applicability, while correcting some erroneous results. We also generalize key results and present new results that contribute to the development of the theory.…
Classical assumptions like strong convexity and Lipschitz smoothness often fail to capture the nature of deep learning optimization problems, which are typically non-convex and non-smooth, making traditional analyses less applicable. This…
Regularized empirical risk minimization with constrained labels (in contrast to fixed labels) is a remarkably general abstraction of learning. For common loss and regularization functions, this optimization problem assumes the form of a…
We consider multi-agent decision making where each agent optimizes its convex cost function subject to individual and coupling constraints. The constraint sets are compact convex subsets of a Euclidean space. To learn Nash equilibria, we…
We consider the closely related problems of bandit convex optimization with two-point feedback, and zero-order stochastic convex optimization with two function evaluations per round. We provide a simple algorithm and analysis which is…
In knowledge graph embedding, the theoretical relationship between the softmax cross-entropy and negative sampling loss functions has not been investigated. This makes it difficult to fairly compare the results of the two different loss…
Min-max problems have broad applications in machine learning, including learning with non-decomposable loss and learning with robustness to data distribution. Convex-concave min-max problem is an active topic of research with efficient…
We investigate a class of composite nonconvex functions, where the outer function is the sum of univariate extended-real-valued convex functions and the inner function is the limit of difference-of-convex functions. A notable feature of…
Many emerging applications - such as adversarial training, AI alignment, and robust optimization - can be framed as zero-sum games between neural nets, with von Neumann-Nash equilibria (NE) capturing the desirable system behavior. While…
In this sequel to a previous paper, we construct certain smooth strongly polyconvex functions $F$ on $\mathbb M^{2\times 2}$ such that $\sigma=DF$ satisfies the Condition (OC) in that paper. As a result, we show that the initial-boundary…
We initiate a program of average smoothness analysis for efficiently learning real-valued functions on metric spaces. Rather than using the Lipschitz constant as the regularizer, we define a local slope at each point and gauge the function…
Cross-entropy is a widely used loss function in applications. It coincides with the logistic loss applied to the outputs of a neural network, when the softmax is used. But, what guarantees can we rely on when using cross-entropy as a…
This paper studies non-smooth problems of convex stochastic optimization. Using the smoothing technique based on the replacement of the function value at the considered point by the averaged function value over a ball (in $l_1$-norm or…
Softmax policy gradient is a popular algorithm for policy optimization in single-agent reinforcement learning, particularly since projection is not needed for each gradient update. However, in multi-agent systems, the lack of central…
Learning complicated value functions in high dimensional state space by function approximation is a challenging task, partially due to that the max-operator used in temporal difference updates can theoretically cause instability for most…
Given a monotone convex function on the space of essentially bounded random variables with the Lebesgue property (order continuity), we consider its extension preserving the Lebesgue property to as big solid vector space of random variables…
Reinforcement Learning (RL) has been widely applied to many control tasks and substantially improved the performances compared to conventional control methods in many domains where the reward function is well defined. However, for many…
The extraction of useful deep features is important for many computer vision tasks. Deep features extracted from classification networks have proved to perform well in those tasks. To obtain features of greater usefulness, end-to-end…