New method speeds up optimization with non-uniform sampling.
problem Optimizing complex stochastic problems efficiently.
method Stochastic Primal Dual Coordinate Method with Optimality Violation-based Sampling.
result The proposed method and variants outperform other methods in speed.
Quantized Stochastic Primal-Dual Methods for Distributed Optimization
problem Distributed optimization with stochastic gradients and finite-bit communication
method q-PDGD, a quantized stochastic primal-dual method
result Linear contraction to an explicit neighborhood under RSI, O(1/k) convergence under PL inequality
We study a stochastic and distributed algorithm for nonconvex problems whose objective consists of a sum of N N N nonconvex L i / N L_i/N L i / N -smooth functions, plus a nonsmooth regularizer. The proposed NonconvEx primal-dual SpliTTing (NESTT) algorithm splits the problem into N N N subproblems, and utilizes an augmented Lagrangian b…
New algorithms solve convex-concave problems faster than previous methods.
problem Solving min-max problems without bilinear structure.
method Stochastic primal-dual algorithms with logarithmic dual updates.
result Faster convergence rates than O ( 1 / T ) O(1/\sqrt{T}) O ( 1/ T ) for certain problems. Improved first-order algorithm for entropy regularized OT with faster convergence.
problem Solving entropy regularized optimal transport efficiently.
method Accelerated primal-dual stochastic mirror descent algorithm with variance reduction.
result Improved rate from O ~ ( n 2.5 / ε ) \widetilde{O}({n^{2.5}}/ε) O ( n 2.5 / ε ) to O ~ ( n 2 / ε ) \widetilde{O}({n^2}/ε) O ( n 2 / ε ) . New algorithm solves composite optimization problems with unknown expectations.
problem Solving composite optimization problems with unknown statistical expectations.
method Proposes a new stochastic primal-dual algorithm for composite optimization problems with unknown statistical expectations.
result Converges to a saddle point of the Lagrangian function.
New SPD methods improve online policy estimation in MDPs with reduced storage and complexity.
problem Online estimation of optimal policies in Markov decision processes (MDPs).
method Stochastic Primal-Dual (SPD) methods that update few coordinates of value and policy estimates.
result SPD methods find absolute- ε ε ε -optimal policies with high probability using a specified number of iterations/samples. Two algorithms solve nonconvex minimax problems with linear constraints, achieving complexity guarantees.
problem Nonconvex minimax problems with coupled linear constraints.
method Zeroth-order primal-dual alternating projected gradient (ZO-PDAPG) and zeroth-order regularized momentum primal-dual projected gradient (ZO-RMPDPG) algorithms.
result Iteration complexity guarantees for solving nonconvex-(strongly) concave minimax problems with coupled linear constraints.
Accelerates machine learning algorithms for sparse data.
problem Efficiently solving composite convex minimization problems.
method Accelerated dual-averaging primal-dual method for composite convex minimization.
result Demonstrates advantages in handling sparse data both theoretically and empirically.
A new algorithm reduces the complexity of solving optimal transport problems.
problem Optimal transport problem with linear constraints.
method Primal-dual accelerated stochastic gradient descent with variance reduction (PDASGD).
result Achieves the best-known computational complexity of O ~ ( n 2 / ε ) \widetilde{\mathcal{O}}(n^2/ε) O ( n 2 / ε ) for OT problems. We propose a doubly stochastic primal-dual coordinate optimization algorithm for empirical risk minimization, which can be formulated as a bilinear saddle-point problem. In each iteration, our method randomly samples a block of coordinates of the primal and dual solutions to update. The linear convergence of our method…
Optimizes stochastic linear bandits with efficient, asymptotically optimal algorithm.
problem Optimizing stochastic linear bandits with multiple actions.
method Frequentist information-directed sampling (IDS) with a surrogate for information gain.
result Asymptotically optimal and nearly worst-case optimal in finite time.
New algorithm speeds up large-scale statistical inference.
problem Efficiently solving large-scale mean-field variational inference problems.
method Developed a novel primal-dual algorithm (PD-VI) and a block-preconditioned extension (P 2 ^2 2 D-VI) for mean-field variational inference. result PD-VI and P 2 ^2 2 D-VI achieve faster convergence and better solution quality compared to existing methods. This work tackles resource allocation in asynchronous and stochastic systems.
problem Distributed resource allocation in asynchronous and stochastic settings.
method Approximate stochastic primal-dual approach with asynchronous updates.
result The Asynchronous stochastic Primal-Dual (Asyn-PD) algorithm converges to the saddle point solution at a rate of O ( 1 / t ) O(1/t) O ( 1/ t ) . Drago optimizes DRO problems with faster convergence.
problem Distributionally robust optimization with closed, convex uncertainty sets.
method Primal-dual coupled variance reduction algorithm with cyclic and randomized updates.
result Achieves state-of-the-art linear convergence rate on strongly convex-strongly concave problems.
Develops an online method for solving constrained optimization problems with debiasing techniques.
problem Online inference of solutions to constrained optimization problems with equality and inequality constraints.
method Stochastic Sequential Quadratic Programming (SSQP) with momentum debiasing.
result Achieves global almost-sure convergence and local asymptotic normality with optimal primal-dual limiting covariance.
We consider convex-concave saddle point problems with a separable structure and non-strongly convex functions. We propose an efficient stochastic block coordinate descent method using adaptive primal-dual updates, which enables flexible parallel optimization for large-scale problems. Our method shares the efficiency an…
Gradient method achieves linear convergence for saddle point problems without strong convexity.
problem Solving saddle point problems with non-strongly convex functions.
method Primal-dual gradient method with a novel analysis technique.
result Linear convergence achieved without strong convexity of f f f . We consider a generic convex-concave saddle point problem with separable structure, a form that covers a wide-ranged machine learning applications. Under this problem structure, we follow the framework of primal-dual updates for saddle point problems, and incorporate stochastic block coordinate descent with adaptive st…
We consider a generic convex optimization problem associated with regularized empirical risk minimization of linear predictors. The problem structure allows us to reformulate it as a convex-concave saddle point problem. We propose a stochastic primal-dual coordinate (SPDC) method, which alternates between maximizing ov…
A new method for distributed optimization reduces communication rounds without minibatches.
problem Efficient training in distributed machine learning with different data distributions.
method A primal-dual method (GA-MSGD) applied to the Lagrangian of distributed optimization.
result Achieves linear convergence in communication rounds for strongly convex objectives.
Estimates bisimulation metrics from sample streams, not full transition models.
problem Estimating Markov chain metrics from limited sample data.
method Stochastic optimization using linear programming and primal-dual method.
result Validated through empirical evaluations, providing sample complexity guarantees.
We generalize the primal-dual methodology, which is popular in the pricing of early-exercise options, to a backward dynamic programming equation associated with time discretization schemes of (reflected) backward stochastic differential equations (BSDEs). Taking as an input some approximate solution of the backward dyn…
New PDHG approach tackles high-cost stochastic minimization with linear composite terms.
problem High cost and lack of closed-form proximal mapping for composite regularization terms.
method Stochastic PDHG with data point sampling, high-probability iteration complexity analysis.
result High-probability convergence analysis supports practical performance.
New algorithm solves saddle point problems in Banach spaces.
problem Solving saddle point problems in real reflexive Banach spaces.
method Stochastic Bregman Primal-Dual Splitting Algorithm with relative smoothness and strong convexity assumptions.
result Almost sure convergence to saddle points under various conditions.
FeDualEx tackles saddle point optimization in federated learning with composite objectives.
problem Saddle point optimization with constraints and non-smooth regularization in federated learning.
method Federated Dual Extrapolation (FeDualEx) algorithm for saddle point optimization and composite objectives.
result FeDualEx effectively solves saddle point optimization problems with composite objectives in federated learning.
A new method uses deep learning for optimal stopping problems.
problem Solving optimal stopping problems in financial mathematics.
method Deep primal-dual BSDE framework with a novel loss function.
result The method provides a true upper bound for the optimal value.
Study efficient convergence of RL algorithm with function approximation.
problem Convergence of actor-critic algorithm with nonlinear function approximation.
method Stochastic gradient descent ascent with adaptive proximal term, Polyak-Łojasiewicz condition.
result First efficient convergence result with rate of O(sqrt{ln(N d G^2) / N}).
In this paper we propose a randomized primal-dual proximal block coordinate updating framework for a general multi-block convex optimization model with coupled objective function and linear constraints. Assuming mere convexity, we establish its O ( 1 / t ) O(1/t) O ( 1/ t ) convergence rate in terms of the objective value and feasibility m…
New method solves constrained stochastic optimization problems efficiently.
problem Online statistical inference of constrained stochastic nonlinear optimization problems.
method Stochastic Sequential Quadratic Programming (StoSQP) with iterative sketching solver.
result The rescaled primal-dual sequence converges to a mean-zero Gaussian distribution.
A new algorithm for decentralized learning in heterogeneous networks reduces sub-optimality over time.
problem Learning in decentralized heterogeneous networks with local data streams and nonlinear constraints.
method Functional variant of stochastic primal-dual method with greedy subspace projection.
result The HALK algorithm achieves O ( T ) \mathcal{O}(\sqrt{T}) O ( T ) sub-optimality reduction and constraint satisfaction. New method learns MDP policies without projections, achieving near optimal results.
problem Learning policies for large MDPs with high sample complexity.
method Projection-free stochastic primal-dual method for approximate linear programming.
result PAC sample complexity analysis and improved efficiency compared to existing methods.
The paper tackles online resource allocation with uncertain coefficients and chance constraints.
problem Online stochastic resource allocation problem with chance constraints.
method Linearization and primal-dual algorithms with heuristic corrections.
result Optimality gap and constraint violation are on the order of √n.
New algorithms exploit data's strong convexity for fast linear convergence without explicit regularization.
problem Empirical risk minimization with convex loss functions.
method Primal-dual first-order algorithms that exploit data's strong convexity.
result Adaptive primal-dual algorithms achieve linear convergence without explicit regularization.
New algorithm solves complex optimization problems with two regularization terms efficiently.
problem Complex optimization problems with two regularization terms, especially composed with linear functions.
method Stochastic Primal-Dual Proximal ExtraGradient descent (SPDPEG) for convex and strongly convex objectives.
result Converges with rates matching best first-order stochastic algorithms.
Paper develops efficient algorithms for robust optimization across multiple groups.
problem Minimizing maximal empirical risk across distinct groups in robust optimization.
method Develops ALEG and ALEM algorithms for two-level finite-sum convex-concave minimax optimization.
result Achieves ε-accuracy with complexity O(m√(nlnm/ε)) and outperforms state-of-the-art methods.
New algorithm reduces regret and constraint violation in adversarial CMDP learning.
problem Online learning for episodic stochastically constrained Markov decision processes (CMDPs) with adversarial loss.
method Upper Confidence Primal-Dual Reinforcement Learning (UC-PDL) algorithm.
result Achieves O ~ ( L ∣ S ∣ ∣ A ∣ T ) \widetilde{\mathcal{O}}(L|\mathcal{S}|\sqrt{|\mathcal{A}|T}) O ( L ∣ S ∣ ∣ A ∣ T ) upper bounds of both regret and constraint violation. 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.
PDCA algorithm learns policies for RL with constraints using a primal-dual approach.
problem Offline constrained reinforcement learning with general function approximation.
method Primal-Dual-Critic Algorithm (PDCA) using a primal-dual approach.
result PDCA finds a near saddle point of the Lagrangian, nearly optimal for constrained RL.
Proposes an online method for solving non-convex DRO with KL regularization.
problem Solving distributionally robust optimization with non-convex objectives.
method Practical online stochastic methods for DRO with KL regularization, avoiding high-dimensional dual variables and online learning issues.
result Empirical studies show significant speedup and efficiency in training deep learning models.
New algorithm minimizes sum of three functions with linear operator.
problem Minimizing the sum of three convex functions with a linear operator.
method Proposes a new primal-dual algorithm for the problem.
result Proves convergence and provides convergence rates.
New method accelerates convergence for entropy-regularized reinforcement learning problems.
problem Slow convergence of standard first-order methods for entropy-regularized Markov decision processes.
method Introduce a quadratically convexified primal-dual formulation and a new interpolating metric to accelerate convergence.
result Global convergence and exponential convergence rate for the new method.
New algorithms improve computation of optimal transport and Wasserstein barycenter.
problem Computing optimal transport and Wasserstein barycenter for multiple probability distributions.
method Introduced APDRCD and APDGCD algorithms for efficient computation, demonstrating better performance than existing methods.
result New algorithms match or exceed the best known complexities for OT problems and improve practical performance.
Cross-learning improves multi-task learning performance.
problem Improving multi-task learning across different domains.
method Coupling parameters across tasks with a stochastic projected gradient algorithm and primal-dual approach.
result Cross-learned functions outperform task-specific and consensus approaches in image classification.
PURE-CD algorithm proves complexity bounds for convex-concave problems.
problem Solving convex-concave min-max problems with bilinear coupling.
method Primal-dual algorithm with random extrapolation and coordinate descent (PURE-CD).
result Complexity bounds match or improve existing results for dense and sparse problems.
New algorithm achieves sublinear regret in CMDPs without error cancellations.
problem Safety constraints in reinforcement learning with error cancellations.
method Model-based primal-dual algorithm for CMDPs with multiple constraints.
result Achieves sublinear regret without error cancellations.
Optimal privacy-preserving algorithm for solving saddle point problems.
problem Solving convex-concave stochastic saddle point problems under differential privacy constraints.
method Recursive regularization technique repurposed for saddle point problems, achieving strong gap rate of O(1/√n + √d/nε).
result Achieves nearly optimal strong gap rate of O(1/√n + √d/nε) with gradient complexity O(min{n^2ε^(1.5)/√d, n^(3/2)}).
A deep neural network improves document binarization accuracy.
problem Binarizing digital documents with historical degradations.
method Combines FCN with primal-dual network for end-to-end training.
result Achieves state-of-the-art binarization on four out of seven datasets.