Paper analyzes SARAH for nonconvex optimization with mini-batches.
problem Solving nonconvex optimization problems with mini-batches.
method Stochastic Recursive Gradient Algorithm (SARAH) for nonconvex losses.
result Sublinear and linear convergence rates for different types of nonconvex functions.
SARAH uses stochastic recursive gradient for efficient machine learning.
problem Finite-sum minimization problems in machine learning.
method SARAH and SARAH+ algorithms with recursive gradient estimates.
result Linear convergence rate proven under strong convexity assumption.
The paper solves utility maximization under partial information using transformations and perturbation methods.
problem Maximizing recursive utility under partial information.
method Transforming to full information, using variational formulation, stochastic game approach, and terminal perturbation method.
result Explicit saddle points and optimal terminal wealth obtained.
Derives a matrix factorisation algorithm from recursive linear filters.
problem Efficient inference in high-dimensional matrix factorisations.
method Probabilistic model and recursive linear filter derivation.
result Interprets the algorithm as a stochastic gradient.
Two new methods reduce OCO problem complexity without projections.
problem Efficiently solving smooth Online Convex Optimization problems without projections.
method ORGFW and MORGFW methods using recursive gradient estimation.
result Achieve optimal regret bounds with low computational costs.
New method finds near-optimal solutions for non-convex optimization problems.
problem Finding near-optimal solutions for non-convex optimization problems.
method Riemannian stochastic recursive momentum method
result Achieves a near-optimal complexity of i l d e O ( ε − 3 ) ilde{\mathcal{O}}(ε^{-3}) i l d e O ( ε − 3 ) . The study analyzes how stochastic recursive algorithms converge to Markov chains.
problem Understanding convergence of stochastic recursive algorithms to Markov chains.
method Analyzes iterated random operators and contraction operators over Polish spaces.
result The distribution of random sequences converges to the invariant distribution of the Markov chain.
A new algorithm SRG-DQN reduces variance in deep Q-learning.
problem Inaccurate estimation of anchor points in SVRG for deep Q-learning.
method Introduces recursive gradient variance reduction for stochastic gradient updates.
result Demonstrates improved efficiency and effectiveness of SRG-DQN on reinforcement learning tasks.
Estimates and optimizes UBSR risk in recursive settings.
problem Estimating and optimizing UBSR risk in a recursive setting with one-at-a-time samples.
method Casts UBSR as a root finding problem, uses stochastic approximation and gradient descent.
result Derives non-asymptotic bounds on estimation and optimization errors.
STORM-PG uses momentum for faster policy gradient updates.
problem Improving policy gradient methods for reinforcement learning.
method Introduces STORM-PG, a SARAH-based algorithm with exponential moving average.
result Achieves O ( 1 / ε 3 ) O(1/ε^3) O ( 1/ ε 3 ) sample complexity, matching best-known rate. Developed moment estimators for affine stochastic volatility models.
problem Estimating parameters of affine stochastic volatility models.
method Introduced recursive equations for moments and proposed moment estimators.
result Established a central limit theorem and derived asymptotic covariance matrix.
Greedy training of recursive partitioning estimators faces a computational barrier when the true function doesn't satisfy a specific property.
problem Computational inefficiency of greedy training for recursive partitioning estimators.
method Analysis of greedy training for sparse regression functions over binary features.
result Greedy training requires exponential samples when the true function doesn't satisfy a specific property (MSP), but only logarithmic samples when it does.
The paper characterizes optimal solutions for utility optimization with stochastic elements.
problem Optimal portfolio optimization under uncertainty.
method Characterization of fully coupled FBSDEs in terms of BSDEs.
result Explicit examples and methods to quantify incompleteness and find optimal solutions.
The paper analyzes a recursive ML estimation method for non-linear state-space models.
problem Estimating maxima of the log-likelihood function in non-linear state-space models.
method Recursive maximum likelihood estimation using particle approximation to the optimal filter derivative.
result The algorithm accurately estimates maxima of the log-likelihood when the number of particles is sufficiently large.
New approach solves utility maximization problems using Delta family.
problem Utility maximization in stochastic control problems.
method Directly solving DP equation with Delta function representation.
result Explicit series representation of value function.
Improved SVRC algorithm reduces complexity for nonconvex optimization.
problem Finding local minima for nonconvex finite-sum optimization with improved complexity.
method Stochastic Recursive Variance-Reduced Cubic regularization (SRVRC) using recursively updated semi-stochastic gradient and Hessian estimators.
result SRVRC achieves improved gradient and Hessian complexities to find ( ε , ε ) (ε, \sqrtε) ( ε , ε ) -approximate local minimum. Researchers study heavy-tail properties of SGD using stochastic recurrence equations.
problem Analyzing heavy-tail properties of Stochastic Gradient Descent (SGD).
method Modeling SGD iterations as multivariate affine stochastic recursions and applying the theory of irreducible-proximal (i-p) matrices.
result Extended results of Gürbüzbalaban et al. (2020) by using the theory of i-p matrices.
Improved accuracy in quantization methods for financial derivatives.
problem Efficient numerical methods for evaluating functionals of stochastic differential equations.
method Recursive Marginal Quantization of higher-order schemes (Euler, Milstein, simplified weak order 2.0).
result Higher-order schemes provide improved weak order convergence and accurate marginal distributions.
Unified framework for analyzing convergence of RSAs using Wasserstein divergence.
problem Analyzing convergence of constant stepsize recursive stochastic algorithms (RSAs).
method Lifting RSA into a higher-dimensional space as a Markov chain and studying the distribution's contraction property with respect to Wasserstein divergence.
result RSAs' iterates' distribution converges to an invariant distribution under certain contraction properties.
Solves optimal stopping problem with Poisson constraints using jumps.
problem Optimal stopping with Poisson constraints and jumps.
method Penalized backward stochastic differential equation (PBSDE) with jumps, decomposition method based on Jacod-Pham, comparison theorem of BSDEs with jumps.
result Solves American option pricing in nonlinear markets with Poisson constraints.
Paper uses averaging from many particle filters to approximate posterior predictive distributions.
problem Approximating posterior predictive distributions efficiently and accurately.
method Particle swarm filter algorithm that averages many particle filter approximations.
result Law of large numbers and central limit theorem support the method's effectiveness.
New algorithm reduces complexity for optimizing complex machine learning tasks.
problem Optimizing complex machine learning objectives like reinforcement learning and portfolio management.
method Developed SARAH-Compositional algorithm using Stochastic Recursive Gradient Descent.
result Achieved optimal IFO complexity bounds for stochastic compositional optimization.
ERM uses energy-based selection to improve recursive reasoning.
problem Lack of principled inference mechanism in recursive models.
method Energy-guided Recursive Model (ERM) introduces Hopfield energies for trajectory selection.
result ERM achieves optimal solutions on various puzzles.
Recursive filtering predicts wireless interference levels accurately.
problem Predicting interference in wireless networks.
method Designing a recursive predictor using Kalman filtering and ARMA model.
result Good accuracy of predicted interference values compared to true values.
Paper develops probabilistic bounds for a stochastic gradient algorithm in non-convex problems.
problem Stochastic optimization in non-convex finite sum problems.
method Develops a new dimension-free Azuma-Hoeffding type bound for a martingale difference sequence.
result Empirical results show superior probabilistic performance of Prob-SARAH compared to other algorithms.
New approach to probabilistic programming inference using particle MCMC.
problem Efficient inference in complex probabilistic models.
method Particle Markov chain Monte Carlo for Turing-complete languages.
result More efficient than single-site Metropolis-Hastings methods.
New method tracks time-varying parameters in data.
problem Tracking unknown time-varying parameters in data.
method Stochastic gradient descent-based recursive scheme with log-likelihood as gain function.
result Convergence in mean-square error in a suitable neighborhood of the unknown parameter.
Study dynamic Pareto-optimal allocations in multi-period economies with time-consistent risk measures.
problem Optimal allocation in multi-period pure-exchange economies with stochastic endowments and time-consistent risk measures.
method Introduced dynamic Pareto-optimal allocation processes and derived recursive and comonotone improvement theorems.
result Dynamic Pareto-optimal allocation processes can be constructed recursively and are comonotone.
Recursive KalmanNet combines neural networks with Kalman filters for precise state estimation.
problem State estimation in systems with noisy measurements and non-Gaussian noise.
method Recursive KalmanNet uses a recurrent neural network to estimate states with consistent error covariance, optimizing for Gaussian negative log-likelihood.
result Recursive KalmanNet outperforms conventional Kalman filters and deep learning-based estimators in non-Gaussian noise conditions.
This work studies the contraction coefficients of Schrödinger bridge problems in linear systems.
problem Optimally controlling the evolution of a system's state density over time.
method Analyzes and improves the convergence rates of dynamic Schrödinger systems via geometric and control-theoretic interpretations.
result New insights into improving computation of worst-case contraction coefficients by preconditioning.
Stochastic discount factor (SDF) processes in dynamic economies admit a permanent-transitory decomposition in which the permanent component characterizes pricing over long investment horizons. This paper introduces an empirical framework to analyze the permanent-transitory decomposition of SDF processes. Specifically, …
Paper finds a new principle for optimizing consumption and wealth using Tsallis entropy.
problem Optimal consumption-investment problem with recursive utility.
method Established connection to quadratic BSDE, derived stochastic maximum principle.
result Proved existence of optimal strategy and analyzed coupled system.
In this paper the stability theorem of Borkar and Meyn is extended to include the case when the mean field is a differential inclusion. Two different sets of sufficient conditions are presented that guarantee the stability and convergence of stochastic recursive inclusions. Our work builds on the works of Benaim, Hofba…
SREDA optimizes complex machine learning problems with fewer evaluations.
problem Finding an optimal point in nonconvex-strongly-concave minimax problems.
method Stochastic Recursive Gradient Descent Ascent (SREDA) with variance reduction.
result Achieves optimal stochastic gradient complexity of O(κ^3ε^-3).
Introduces a new theoretical framework for exponential smoothing.
problem Theoretical foundation and robustness of simple exponential smoothing.
method Stochastic gradient ascent to optimize Gaussian log-likelihood functions.
result Simple exponential smoothing converges to the trend of a trend-stationary process.
DESTRESS optimizes decentralized nonconvex optimization with optimal IFO complexity and efficient communication.
problem Decentralized nonconvex finite-sum optimization in multi-agent systems.
method DESTRESS uses stochastic recursive gradient updates, gradient tracking, and careful hyper-parameter choices to achieve optimal IFO complexity with efficient communication.
result DESTRESS matches the optimal IFO complexity of centralized algorithms while maintaining communication efficiency.
Paper develops a high-order recombination algorithm for financial modeling.
problem Creating accurate approximations of stochastic differential equations in finance.
method High-order recombination method applied to practical financial problems.
result Algorithm effectively avoids explosive growth in support cardinality for high-order approximations.
We propose an explicit recursive method to approximate a power-law with a finite sum of weighted exponentials. Applications to moving averages with long memory are discussed in relationship with stochastic volatility models.
Proposes a recursive MPC scheme with probabilistic safety guarantees for uncertain dynamic systems.
problem Probabilistic safety guarantees for MPC in dynamic environments with unknown stochastic agents.
method Uses conformal prediction to derive high-confidence prediction regions and gradually relax safety constraints online.
result Ensures recursive feasibility of MPC schemes by relaxing safety constraints over time.
Expands Thiele equation for non-Markovian life insurance cash flows.
problem Circular dependency in life insurance cash flows and reserves.
method Expands Thiele equation to non-Markovian frameworks and presents a recursive scheme.
result Calculates multiple contract modifications in non-Markovian life insurance.
Paper introduces XBART for nonlinear regression, outperforming XGBoost.
problem Nonlinear regression problems, especially in speed and accuracy.
method Combines Bayesian modeling and recursive partitioning for efficient, accurate predictions.
result XBART provides faster and more accurate predictions than XGBoost.
Paper applies quantization to polynomial processes for option pricing.
problem Quantization for polynomial processes in finance.
method Two quantization procedures for stochastic volatility Jacobi process.
result Theoretical and practical tools for fast option pricing.
AdaVol adapts QML for real-time GARCH volatility prediction.
problem Real-time estimation of GARCH volatility in streaming data.
method Adaptive recursive estimation routine with Variance Targeting Estimation.
result AdaVol provides a stable and adaptive method for real-life data.
Paper develops efficient methods for estimating Hessian inverses in stochastic optimization.
problem Estimating the inverse Hessian for convex function minimization.
method Robbins-Monro procedure for recursive estimation of the inverse Hessian.
result Develops universal stochastic Newton methods with improved efficiency.
Recursive KalmanNet generalizes well in noisy, out-of-distribution scenarios.
problem Generalization in noisy, out-of-distribution scenarios.
method Recurrent neural network guided by a Kalman filter.
result Recursive KalmanNet performs well in scenarios with different temporal dynamics from training data.
Paper avoids strict saddles in stochastic optimization without UE assumption.
problem Avoiding strict saddles in stochastic optimization without uniform positive excitation.
method Pathwise Lyapunov-Perron framework, local smoothness, finite-moment assumptions.
result Avoidance of strict saddles for stochastic mirror descent and proximal-type methods.
We expand volatility models for rough stochastic volatility.
problem Modeling rough stochastic volatility.
method Vol-of-vol expansion for potentially infinite dimensional models.
result Explicit representations of push-down Malliavin weights.
Online (also called "recursive" or "adaptive") estimation of fixed model parameters in hidden Markov models is a topic of much interest in times series modelling. In this work, we propose an online parameter estimation algorithm that combines two key ideas. The first one, which is deeply rooted in the Expectation-Maxim…