Dual averaging-type methods are widely used in industrial machine learning applications due to their ability to promoting solution structure (e.g., sparsity) efficiently. In this paper, we propose a novel accelerated dual-averaging primal-dual algorithm for minimizing a composite convex function. We also derive a stoch…
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48 results for “dual averaging”
New algorithm for federated learning with non-smooth regularizers.
problem Federated Learning with non-smooth composite optimization problems.
method Proposed Federated Dual Averaging (FedDualAvg) algorithm to overcome convergence issues.
result FedDualAvg outperforms other algorithms in federated composite optimization.
DSPI connects natural policy gradient to policy iteration, proving global convergence.
problem Optimizing policies in reinforcement learning.
method DSPI framework, combining smoothed policy iteration and natural policy gradient.
result DSPI achieves geometric convergence and optimal complexity for policy optimization.
PDA method optimizes neural networks with global convergence rate analysis.
problem Quantitative convergence rate for neural network optimization in mean field regime.
method Particle dual averaging (PDA) method, combining Langevin algorithm and outer loop optimization.
result Established quantitative global convergence for two-layer mean field neural networks.
Despite the success of single-agent reinforcement learning, multi-agent reinforcement learning (MARL) remains challenging due to complex interactions between agents. Motivated by decentralized applications such as sensor networks, swarm robotics, and power grids, we study policy evaluation in MARL, where agents with jo…
We consider a composite convex minimization problem associated with regularized empirical risk minimization, which often arises in machine learning. We propose two new stochastic gradient methods that are based on stochastic dual averaging method with variance reduction. Our methods generate a sparser solution than the…
New method tackles composite optimization with error feedback.
problem Challenges in distributed machine learning training and message compression.
method Combines Dual Averaging with EControl for composite optimization.
result First strong convergence analysis for composite optimization with error feedback.
This dissertation advances the theoretical foundation of local optimization methods in Federated Learning.
problem Theoretical understanding of local optimization methods in Federated Learning is lacking.
method The dissertation proposes and analyzes new methods to improve convergence rates and communication efficiency in Federated Learning.
result Sharp bounds and convergence rates for FedAvg are established, and new methods like FedAc and Federated Dual Averaging are proposed.
MDA optimizer performs similarly to SGD+M in CV and Adam in NLP.
problem Performance degradation due to choosing the wrong optimizer.
method Modernized Dual Averaging (MDA) optimizer, inspired by dual averaging.
result MDA performs as well as SGD+M in CV and as Adam in NLP.
In decentralized networks (of sensors, connected objects, etc.), there is an important need for efficient algorithms to optimize a global cost function, for instance to learn a global model from the local data collected by each computing unit. In this paper, we address the problem of decentralized minimization of pairw…
Paper develops Byzantine-resilient algorithms for decentralized learning.
problem Vulnerability of distributed learning to Byzantine attacks.
method Dual approach for decentralized optimization.
result Convergence guarantees and experimental validation of the proposed algorithm.
OMD and DA perform similarly in static settings but OMD is inferior under dynamic learning rates.
problem Proving and understanding the performance difference between OMD and DA under dynamic learning rates.
method Introducing stabilization to OMD and modifying its convergence analysis.
result OMD with stabilization and DA have the same performance guarantees under dynamic learning rates.
Discrete normal surfaces are normal surfaces whose intersection with each tetrahedron of a triangulation has at most one component. They are also natural Poincaré duals to 1-cocycles with $\ZZ/2\ZZ$-coefficients. For a fixed cohomology class in a simplicial poset the average Euler characteristic of the associated discr…
This paper introduces metrics for welfare analysis in dynamic models. We develop estimation and inference for these parameters even in the presence of a high-dimensional state space. Examples of welfare metrics include average welfare, average marginal welfare effects, and welfare decompositions into direct and indirec…
We propose a voted dual averaging method for online classification problems with explicit regularization. This method employs the update rule of the regularized dual averaging (RDA) method, but only on the subsequence of training examples where a classification error is made. We derive a bound on the number of mistakes…
Study on Santaló point for convex bodies in normed spaces.
problem Exploring Santaló point for convex bodies in normed spaces.
method Existence and uniqueness proof for norms, dual Santaló point for smooth curved unit balls.
result Existence and uniqueness of Santaló point for convex bodies in normed spaces.
New approach shapes error distribution in long-term forecasting.
problem Disparate error distributions in recent transformer models.
method Loss shaping constraints to respect upper bounds on loss at each time-step.
result Competitive average performance with shaped error distribution.
Develops a new method for robust risk measurement by averaging nearby payoffs.
problem Measuring risk under uncertainty with a focus on robustness.
method Averaging nearby payoffs weighted by a chosen metric.
result The method leads to a convex risk measure and provides stability under large neighborhoods.
New algorithms optimize spectral risk measures, improving interpolation between average and worst-case performance.
problem Optimizing spectral risk measures for learning systems.
method Developed stochastic algorithms to optimize spectral risk measures by characterizing their subdifferential and addressing challenges like biasedness of subgradient estimates and non-smoothness.
result Our approach outperforms out-of-the-box stochastic subgradient and dual averaging methods in optimizing spectral risk measures.
In this work we develop a new algorithm for regularized empirical risk minimization. Our method extends recent techniques of Shalev-Shwartz [02/2015], which enable a dual-free analysis of SDCA, to arbitrary mini-batching schemes. Moreover, our method is able to better utilize the information in the data defining the ER…
The Ricci tensor (Ric) is fundamental to Einstein's geometric theory of gravitation. The 3-dimensional Ric of a spacelike surface vanishes at the moment of time symmetry for vacuum spacetimes. The 4-dimensional Ric is the Einstein tensor for such spacetimes. More recently the Ric was used by Hamilton to define a non-li…
This paper advances FL algorithms for composite optimization and statistical recovery.
problem Federated learning optimization and statistical recovery in composite settings.
method Proposes Fast Federated Dual Averaging for strongly convex and smooth loss, and Multi-stage Federated Dual Averaging for restricted strongly convex and smooth loss.
result Establishes state-of-the-art iteration and communication complexity, and high probability complexity bound with linear speedup.
Using holographic renormalization coupled with the Caffarelli/Silvestre\cite{caffarelli} extension theorem, we calculate the precise form of the boundary operator dual to a bulk scalar field rather than just its average value. We show that even in the presence of interactions in the bulk, the boundary operator dual to …
A State-Augmented Approach for Learning Optimal Resource Management Decisions in Wireless Networkscs.LG
Optimizes wireless network resource management with state-augmented policies.
problem Optimizing network-wide utility with user performance constraints.
method State-augmented parameterization of RRM policy, using dual variables.
result Superior trade-off between mean, minimum, and 5th percentile rates.
New method uses LP to achieve optimal sample complexity in multi-agent reinforcement learning.
problem Achieving global optimality in multi-agent reinforcement learning with average-cost criterion.
method Randomized Linear Programming and Stochastic Primal-Dual Methods for multi-agent saddle point problems.
result Sample complexity matches tight dependencies on state and action spaces, and scales with network size.
Communication remains the most significant bottleneck in the performance of distributed optimization algorithms for large-scale machine learning. In this paper, we propose a communication-efficient framework, CoCoA, that uses local computation in a primal-dual setting to dramatically reduce the amount of necessary comm…
We propose a general framework for entropy-regularized average-reward reinforcement learning in Markov decision processes (MDPs). Our approach is based on extending the linear-programming formulation of policy optimization in MDPs to accommodate convex regularization functions. Our key result is showing that using the …
Primal-Dual Wasserstein GANstat.ML
We introduce Primal-Dual Wasserstein GAN, a new learning algorithm for building latent variable models of the data distribution based on the primal and the dual formulations of the optimal transport (OT) problem. We utilize the primal formulation to learn a flexible inference mechanism and to create an optimal approxim…
The goal of decentralized optimization over a network is to optimize a global objective formed by a sum of local (possibly nonsmooth) convex functions using only local computation and communication. It arises in various application domains, including distributed tracking and localization, multi-agent co-ordination, est…
Simplicial Ricci Flowmath.DG
We construct a discrete form of Hamilton's Ricci flow (RF) equations for a d-dimensional piecewise flat simplicial geometry, S. These new algebraic equations are derived using the discrete formulation of Einstein's theory of general relativity known as Regge calculus. A Regge-Ricci flow (RRF) equation is naturally asso…
Paper tackles class-incremental time series classification with dual-stream feature extraction.
problem Class-incremental continual learning for multivariate time series data.
method Dual-stream feature extraction pipeline combining deep temporal embedding features and statistical features.
result Competitive average accuracy across multiple datasets with low forgetting rates.
In this paper we present an optimization-based view of distributed parameter estimation and observational social learning in networks. Agents receive a sequence of random, independent and identically distributed (i.i.d.) signals, each of which individually may not be informative about the underlying true state, but the…
This research develops a dual-level reinforcement learning strategy to track daily VWAP accurately.
problem Inaccurate tracking of daily VWAP due to short trading horizons.
method Dual-level architecture using Transformer and LSTM models.
result Improves accuracy in approximating daily VWAP compared to previous models.
We propose an computational framework for real-time risk assessment and prioritizing for random outcomes without prior information on probability distributions. The basic model is built based on satisficing measure (SM) which yields a single index for risk comparison. Since SM is a dual representation for a family of r…
New algorithms optimize without knowing problem parameters.
problem Optimizing large-scale problems without knowing key parameters.
method Combining mirror descent with dual averaging techniques.
result Converges without prior knowledge of problem parameters.
Framework explains how dual deep networks learn features from unlabeled data.
problem Understanding self-supervised learning with dual deep networks.
method Theoretical framework and hierarchical latent tree model.
result Deep ReLU networks learn latent variables through contrastive SSL.
Discretizations of the mean curvature and extrinsic curvature components are constructed on piecewise flat simplicial manifolds, giving approximations for smooth curvature values in a mostly mesh-independent way. These constructions are given in combinatoric form in terms of the extrinsic hinge angles, the intrinsic st…
New algorithm optimizes stochastic optimization with circular dependency.
problem Circular dependency between decision variable and importance sampling.
method Single-loop stochastic approximation algorithm based on Nesterov's dual averaging.
result Achieves minimal asymptotic variance and resolves circular optimization challenge.
Two signature-based methods solve optimal stopping in non-Markovian frameworks.
problem Optimal stopping in non-Markovian frameworks, particularly pricing American options.
method Primal and dual formulations using linear functionals of rough path signatures.
result Both primal and dual methods converge and provide numerical examples.
Learning optimal resource allocation policies in wireless systems can be effectively achieved by formulating finite dimensional constrained programs which depend on system configuration, as well as the adopted learning parameterization. The interest here is in cases where system models are unavailable, prompting method…
Online learning algorithms update models via one sample per iteration, thus efficient to process large-scale datasets and useful to detect malicious events for social benefits, such as disease outbreak and traffic congestion on the fly. However, existing algorithms for graph-structured models focused on the offline set…
We consider the problem of accelerating distributed optimization in multi-agent networks by sequentially adding edges. Specifically, we extend the distributed dual averaging (DDA) subgradient algorithm to evolving networks of growing connectivity and analyze the corresponding improvement in convergence rate. It is know…
We propose a fully distributed actor-critic algorithm approximated by deep neural networks, named \textit{Diff-DAC}, with application to single-task and to average multitask reinforcement learning (MRL). Each agent has access to data from its local task only, but it aims to learn a policy that performs well on average …
In this work we consider optimal stopping problems with conditional convex risk measures called optimised certainty equivalents. Without assuming any kind of time-consistency for the underlying family of risk measures, we derive a novel representation for the solution of the optimal stopping problem. In particular, we …
Radio on Free Space Optics (RoFSO), as a universal platform for heterogeneous wireless services, is able to transmit multiple radio frequency signals at high rates in free space optical networks. This paper investigates the optimal design of power allocation for Wavelength Division Multiplexing (WDM) transmission in Ro…
In this paper we study several classes of stochastic optimization algorithms enriched with heavy ball momentum. Among the methods studied are: stochastic gradient descent, stochastic Newton, stochastic proximal point and stochastic dual subspace ascent. This is the first time momentum variants of several of these metho…
A new parallel algorithm for learning optimal policies in MDPs with low communication costs.
problem Learning optimal policies for infinite-horizon MDPs.
method Primal-Dual Stochastic Mirror Descent for convex programming problems with inexact constraints.
result First parallel algorithm for average-reward MDPs with generative model and low communication costs.
Paper studies optimal tracking portfolio in mean field game of large fund competition.
problem Optimal tracking portfolio in large fund competition with relative performance benchmark.
method Formulated mean field game problem, established existence of mean field equilibrium using PDE approach, constructed approximate Nash equilibrium.
result Existence of mean field equilibrium and consistency condition verified.