Develops parameter-free online mirror descent for optimal dynamic regret.
problem Optimal online linear optimization in unbounded domains.
method Modified online mirror descent framework for parameter-free algorithms.
result First unconstrained online linear optimization achieving optimal dynamic regret.
Fast algorithm for online optimization on transport polytopes.
problem Optimizing convex objectives on transport polytopes.
method Mirror Sinkhorn algorithm combining Sinkhorn scaling and mirror descent.
result Robust and efficient online optimization for convex objectives.
Unified analysis of online optimization with self-concordant barriers, improving regret bounds.
problem Online convex optimization with specific loss functions.
method Online mirror descent with self-concordant barriers and logarithmic loss.
result Improved regret bounds for online portfolio selection and quantum state learning.
A standard introduction to online learning might place Online Gradient Descent at its center and then proceed to develop generalizations and extensions like Online Mirror Descent and second-order methods. Here we explore the alternative approach of putting Exponential Weights (EW) first. We show that many standard meth…
In this paper we consider online mirror descent (OMD) algorithms, a class of scalable online learning algorithms exploiting data geometric structures through mirror maps. Necessary and sufficient conditions are presented in terms of the step size sequence { η t } t \{η_t\}_{t} { η t } t for the convergence of an OMD algorithm with respe…
New algorithm for reinforcement learning reduces complexity and guarantees convergence.
problem Reinforcement learning problems with convex occupancy measures.
method MD-CURL, inspired by mirror descent, uses non-standard regularization.
result Achieves convergence guarantees and simple closed-form solution.
This paper explores a new framework for reinforcement learning based on online convex optimization, in particular mirror descent and related algorithms. Mirror descent can be viewed as an enhanced gradient method, particularly suited to minimization of convex functions in highdimensional spaces. Unlike traditional grad…
Gradient equilibrium improves online learning performance without requiring sublinear regret.
problem Achieving sublinear regret in online learning.
method Gradient equilibrium: average of gradients converges to zero.
result Gradient equilibrium can be achieved by standard online learning methods.
New framework uses tempered optimism to handle imperfect experts in online learning.
problem Challenges of implicit optimism in practical online learning environments.
method Introduces tempered optimism as a framework for online non-convex learning, modifies existing algorithms.
result Demonstrates tempered optimism as a fruitful paradigm for online non-convex learning.
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.
The information-theoretic analysis by Russo and Van Roy (2014) in combination with minimax duality has proved a powerful tool for the analysis of online learning algorithms in full and partial information settings. In most applications there is a tantalising similarity to the classical analysis based on mirror descent.…
Banker-OMD improves online learning with delayed feedback.
problem Handling delayed feedback in online learning.
method Generalized Online Mirror Descent (OMD) framework.
result Achieves nearly-optimal performance in three bandit scenarios.
Study shows Stochastic Mirror Descent optimizes convex problems with infinite noise variance.
problem Optimizing convex problems with infinite noise variance.
method Stochastic Mirror Descent algorithm with uniformly convex mirror maps.
result Demonstrates convergence rate quantified in terms of iterations, dimensionality, and geometric parameters.
This work addresses decentralized online optimization in non-stationary environments. A network of agents aim to track the minimizer of a global time-varying convex function. The minimizer evolves according to a known dynamics corrupted by an unknown, unstructured noise. At each time, the global function can be cast as…
A smart method predicts and optimizes decisions online with resource constraints.
problem Online decision-making with resource constraints.
method Combines prediction and optimization with dual update using mirror descent.
result Regret bounds and convergence rates for general convex feasible regions.
In this paper, we consider the problem of prediction with expert advice in dynamic environments. We choose tracking regret as the performance metric and develop two adaptive and efficient algorithms with data-dependent tracking regret bounds. The first algorithm achieves a second-order tracking regret bound, which impr…
New algorithm for online learning in episodic MDPs with convex objectives.
problem Online episodic convex reinforcement learning.
method Online mirror descent algorithm with varying constraint sets and exploration bonus.
result Near-optimal regret bounds for online CURL without prior knowledge of transition function.
Proposes a new algorithm for robust learning in Schrödinger bridge problems.
problem Uncertainty in estimated learning signals in Schrödinger bridge problems.
method Variational Online Mirror Descent (OMD) framework for Schrödinger bridge problems.
result Formally proves convergence and a regret bound for the OMD formulation of Schrödinger bridge acquisition.
New algorithm tackles adversarial bandits with arbitrary strategies.
problem Adversarial bandit problem against arbitrary strategies.
method Adopted master-base framework using online mirror descent method (OMD). Proposed adaptive learning rates for OMD.
result Achieved improved regret bounds compared to previous methods.
Most traditional online learning algorithms are based on variants of mirror descent or follow-the-leader. In this paper, we present an online algorithm based on a completely different approach, tailored for transductive settings, which combines "random playout" and randomized rounding of loss subgradients. As an applic…
Algorithm for online decision making with unknown dynamics and aggregate feedback.
problem Online decision making with unknown dynamics and aggregate bandit feedback.
method Developed an algorithm based on online mirror descent with a self-concordant barrier regularization and an increasing learning rate schedule.
result Achieved O ( K ) O(\sqrt{K}) O ( K ) regret for the online Markov Decision Process with K K K episodes. Adaptive OMD reduces variance in learning optimal strategies for imperfect information games.
problem High variance in learning optimal strategies for imperfect information games.
method Fixed sampling approach with locally applied Online Mirror Descent (OMD) algorithm.
result Convergence rate of i l d e O ( T − 1 / 2 ) ilde{\mathcal{O}}(T^{-1/2}) i l d e O ( T − 1/2 ) with high probability. OSAMD adapts online to changing distributions with limited labels.
problem Models struggle with continual distribution shifts and expensive labeling in changing environments.
method Online Active Continual Adaptation with OSAMD, an online teacher-student structure and margin-based criterion.
result OSAMD achieves favorable dynamic regret bounds under changing environments with limited labels.
Derives Mirror Descent from gradient flow on a Riemannian manifold.
problem No specific problem stated; focuses on derivation.
method Derives Mirror Descent from gradient flow on a Riemannian manifold with a natural discretization.
result Generalizes Mirror Descent to non-Hessian metrics.
Paper addresses inefficiency in converting EFGs to NFGs for learning.
problem Inefficiency in converting Extensive-Form Games to Normal-Form Games.
method Uses Φ Φ Φ -Hedge algorithm and Online Mirror Descent (OMD) for polynomial-time learning of EFGs. result Achieves O ~ ( X A T ) \widetilde{\mathcal{O}}(\sqrt{XAT}) O ( X A T ) EFCE-regret, matching information-theoretic lower bound. Reparameterizes mirror descent as gradient descent for efficient sparse learning.
problem Efficiently training small sparse networks with mirror descent.
method Develops a framework to convert mirror descent updates into gradient descent updates on different parameters.
result Mirror descent can be reparameterized as gradient descent on modified parameters, facilitating standard backpropagation.
OMWU shows last iterate convergence in convex-concave games.
problem Optimizing in constrained min-max optimization landscapes.
method OMWU (Optimistic Multiplicative-Weights Update) in the no-regret online learning framework.
result OMWU exhibits last iterate convergence for convex-concave games, generalizing previous results.
New analysis shows GMD can converge linearly under PL-like conditions.
problem Establishing linear convergence for generalized mirror descent.
method PL-based analysis for time-dependent mirrors, Taylor-series approach for stochastic GMD.
result Linear convergence of stochastic GMD under PL-like conditions.
Online convex optimization is a sequential prediction framework with the goal to track and adapt to the environment through evaluating proper convex loss functions. We study efficient particle filtering methods from the perspective of such a framework. We formulate an efficient particle filtering methods for the non-st…
Algorithm learns NE in imperfect information games with imperfect feedback.
problem Learning Nash equilibrium in imperfect information games with bandit feedback.
method IXOMD algorithm for model-free learning with 1 / T 1/\sqrt{T} 1/ T convergence rate. result IXOMD achieves 1 / T 1/\sqrt{T} 1/ T convergence rate to NE. New algorithm for nonstationary GLBs reduces computation and memory costs.
problem Nonstationary generalized linear bandits with unknown time-varying parameters.
method Discounted Online Mirror Descent (DOMD) for parameter estimation.
result Dynamic regret bounds of order O ( 1 ) O(1) O ( 1 ) per round in drifting and piecewise-stationary environments. Unified meta-algorithm improves average performance across similar tasks in adversarial bandits.
problem Improving performance across multiple similar tasks in adversarial bandit settings.
method Unified meta-algorithm for multi-armed bandits and bandit linear optimization, tuning initialization, step-size, and entropy parameters.
result Unified meta-algorithm yields setting-specific guarantees for MAB and BLO, improving task-averaged regret.
Improved reinforcement learning algorithm with linear approximation for unknown dynamics.
problem Reinforcement learning with adversarial changing cost functions and bandit feedback.
method Combines mirror-descent and least squares policy evaluation in an auxiliary MDP.
result Obtains an O ~ ( K 6 / 7 ) \widetilde O(K^{6/7}) O ( K 6/7 ) regret bound, significantly improving over previous methods. New algorithm reduces regret and constraint violation in online convex optimization with complex constraints.
problem Online convex optimization with multiple functional constraints and a simple constraint set.
method Instance-dependent bound using online primal-dual mirror-prox algorithm in general normed spaces.
result Achieves an O(√V*(T)) regret and O(1) constraint violation, improving over previous works.
New algorithm reduces optimization complexity in adaptive mirror descent.
problem Optimizing complex, non-smooth, non-convex functions efficiently.
method SVRAMD: Variance Reduced Adaptive Mirror Descent.
result Variance reduction accelerates convergence in adaptive mirror descent.
Mirror descent algorithm recovers low-rank matrices in matrix sensing.
problem Matrix sensing with low-rank matrices under certain conditions.
method Discrete-time mirror descent applied to empirical risk with Bregman divergence analysis.
result Mirror descent converges to a matrix minimizing a specific nuclear norm-related quantity.
Continuous-time mirror descent solves sparse phase retrieval efficiently.
problem Recovering sparse signals from magnitude-only measurements.
method Continuous-time mirror descent applied to unconstrained empirical risk minimization problem.
result Mirror descent recovers k k k -sparse vectors with minimum non-zero entry order of ∥ x ⋆ ∥ 2 / k \| \mathbf{x}^\star \|_2/\sqrt{k} ∥ x ⋆ ∥ 2 / k from k 2 k^2 k 2 Gaussian measurements. Algorithm learns expert weights to minimize regret in adversarial setting.
problem Learning to aggregate expert forecasts with no-regret guarantee in adversarial conditions.
method Online mirror descent algorithm for logarithmic pooling of expert forecasts.
result Achieves O ( T log T ) O(\sqrt{T} \log T) O ( T log T ) expected regret compared to best weights. Two new RL methods enable deep learning of MFG equilibria.
problem Efficiently learning equilibria in Mean Field Games using RL.
method Two novel RL methods: distillation and online mixing.
result Deep RL algorithms can now solve various MFGs.
Mirror descent linked to information ratio via Bayesian regret bounds.
problem Understanding stability in mirror descent and its relation to information ratio.
method Developed a connection between mirror descent and information ratio using Bayesian regret bounds.
result Mirror descent with suitable estimators and distributions achieves bounds similar to information-directed sampling.
The paper connects tempering and entropic mirror descent for sampling.
problem Sampling from a target distribution with known unnormalized density.
method Establishes the connection between tempering SMC and entropic mirror descent, deriving convergence rates and geometric insights.
result Tempering SMC iterates correspond to entropic mirror descent on the reverse KL divergence, providing new optimization perspectives.
Paper studies early-stopped mirror descent for noisy sparse phase retrieval.
problem Recovering a sparse signal from noisy quadratic measurements.
method Early-stopped mirror descent with hyperbolic entropy mirror map.
result Achieves nearly minimax-optimal rate of convergence for k k k -sparse signals. Continuous-time distributed mirror descent with integral feedback converges to global optimum.
problem Distributed optimization of a global strongly convex function with local convex components.
method Continuous-time distributed mirror descent with integral feedback.
result Asymptotic convergence to global optimum with constant step-size.
New method for RLHF reduces costs by integrating new data in one pass.
problem Continuous integration and re-optimization of models in RLHF leads to high computational and storage costs.
method Proposes a one-pass reward modeling method using online mirror descent with a tailored local norm.
result Achieves constant-time updates per iteration, enhancing both statistical and computational efficiency.
This paper extends Mirror Descent to Riemannian manifolds for optimization.
problem Optimization on Riemannian manifolds.
method Developed a Riemannian Mirror Descent (RMD) framework and a stochastic variant.
result Established non-asymptotic convergence guarantees for RMD and stochastic RMD.
Paper uses Mirror Descent for efficient risk budgeting portfolios.
problem Computing optimal risk budgeting weights for various risk measures.
method Employed Mirror Descent algorithms in deterministic and stochastic settings.
result Established convergence and quantitative rate for averaged Mirror Descent algorithm.
Proposes φ φ φ -balancing for more balanced expert utilization in MoE models.
problem Balanced expert utilization in MoE models to avoid bias.
method Directly targets population-level balance by minimizing a convex potential function.
result Consistently outperforms prior methods in stability and effectiveness.
Information geometry applies concepts in differential geometry to probability and statistics and is especially useful for parameter estimation in exponential families where parameters are known to lie on a Riemannian manifold. Connections between the geometric properties of the induced manifold and statistical properti…