Related papers: Convergence of Online Mirror Descent

We present a new perspective on online learning that we refer to as gradient equilibrium: a sequence of iterates achieves gradient equilibrium if the average of gradients of losses along the sequence converges to zero. In general, this…

We consider Online Convex Optimization (OCO) in the setting where the costs are $m$-strongly convex and the online learner pays a switching cost for changing decisions between rounds. We show that the recently proposed Online Balanced…

This work focuses on the setting of dynamic regret in the context of online learning with full information. In particular, we analyze regret bounds with respect to the temporal variability of the loss functions. By assuming that the…

Classical optimisation theory guarantees monotonic objective decrease for gradient descent (GD) when employed in a small step size, or ``stable", regime. In contrast, gradient descent on neural networks is frequently performed in a large…

Multi-objective learning (MOL) aims to learn under multiple potentially conflicting objectives and strike a proper balance. While recent preference-guided MOL methods often rely on additional optimization objectives or constraints, we…

The logarithmic divergence is an extension of the Bregman divergence motivated by optimal transport and a generalized convex duality, and satisfies many remarkable properties. Using the geometry induced by the logarithmic divergence, we…

We develop a gradient-like algorithm to minimize a sum of peer objective functions based on coordination through a peer interconnection network. The coordination admits two stages: the first is to constitute a gradient, possibly with…

Driven by the empirical success and wide use of deep neural networks, understanding the generalization performance of overparameterized models has become an increasingly popular question. To this end, there has been substantial effort to…

As the problem of minimizing functionals on the Wasserstein space encompasses many applications in machine learning, different optimization algorithms on $\mathbb{R}^d$ have received their counterpart analog on the Wasserstein space. We…

Inspired by the recent paper (L. Ying, Mirror descent algorithms for minimizing interacting free energy, Journal of Scientific Computing, 84 (2020), pp. 1-14),we explore the relationship between the mirror descent and the variable metric…

Convergence of the gradient descent algorithm has been attracting renewed interest due to its utility in deep learning applications. Even as multiple variants of gradient descent were proposed, the assumption that the gradient of the…

Distributed optimization often requires finding the minimum of a global objective function written as a sum of local functions. A group of agents work collectively to minimize the global function. We study a continuous-time decentralized…

Follow-the-Regularized-Lead (FTRL) and Online Mirror Descent (OMD) are regret minimization algorithms for Online Convex Optimization (OCO), they are mathematically elegant but less practical in solving Extensive-Form Games (EFGs).…

The convergence of stochastic gradient descent is highly dependent on the step-size, especially on non-convex problems such as neural network training. Step decay step-size schedules (constant and then cut) are widely used in practice…

The minimax excess risk optimization (MERO) problem is a new variation of the traditional distributionally robust optimization (DRO) problem, which achieves uniformly low regret across all test distributions under suitable conditions. In…

We consider risk-averse convex stochastic programs expressed in terms of extended polyhedral risk measures. We derive computable confidence intervals on the optimal value of such stochastic programs using the Robust Stochastic Approximation…

We consider the problem of minimization of a convex function on a simple set with convex non-smooth inequality constraint and describe first-order methods to solve such problems in different situations: smooth or non-smooth objective…

Guided policy search algorithms can be used to optimize complex nonlinear policies, such as deep neural networks, without directly computing policy gradients in the high-dimensional parameter space. Instead, these methods use supervised…

We consider the problem of simultaneously learning to linearly combine a very large number of kernels and learn a good predictor based on the learnt kernel. When the number of kernels $d$ to be combined is very large, multiple kernel…

Relative smoothness - a notion introduced by Birnbaum et al. (2011) and rediscovered by Bauschke et al. (2016) and Lu et al. (2016) - generalizes the standard notion of smoothness typically used in the analysis of gradient type methods. In…