Portfolio Optimization

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5 papers in the last four weeks, against 2 the four weeks before. 0.1% of all new papers.

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Latest papers 32

Oct 1, 2026math.OC

Optimal Momentum Methods for Stochastic Multilevel Compositional Optimization

This paper investigates stochastic multi-level optimization where the objective is a nested composition of several smooth non-convex functions. We assume that only stochastic estimates of the gradient and function values for each level are accessible. Consequently, obtaining an accurate estimate of the overall gradient is challenging due to the nested structure. To address this, we employ a momentum-based estimator with mini-batches to track the function values of each level, which are subsequently used to construct momentum gradient estimators. We establish an optimal sample complexity of

\mathcal{O}(ε^{-4})

for finding an

ε

-stationary point, avoiding the stronger average smoothness assumption commonly relied upon in prior literature. Furthermore, by employing a normalization technique, we attain the same rate without requiring problem-dependent constants to set hyperparameters. To achieve the optimal rate without mini-batches, we further develop a batch-free method that incorporates a first-order approximation and a clipping technique for function value estimation. Finally, we validate the effectiveness of our proposed methods through experiments on risk-averse portfolio optimization and hierarchical tilted empirical risk minimization.

Wei Jiang, Rui Yan, Sifan Yang +3

School of Computer Science and Engineering, Nanjing University of Science and Technology, Nanjing, China · School of Artificial Intelligence, Nanjing University, Nanjing, China · School of Software Technology, Zhejiang University, Ningbo, China

Stochastic Optimization Portfolio Optimization

Sep 28, 2026cs.LG

Retrieval-Augmented Diffusion Modeling for Stochastic Discount Factor Portfolios

In this work, we study portfolio optimization under the stochastic discount factor (SDF) framework by learning market state representations that capture the underlying risk structures of financial data. This is challenging due to several factors: financial markets exhibit non-stationary dynamics with shifting regimes, multimodal inputs such as price and news data often contain stochastic noise, and existing diffusion-based approaches, while effective for modeling stochastic dynamics, rely on assumptions such as isotropic Gaussian noise that fail to capture the state-dependent nature of financial uncertainty. To address these challenges, we introduce RADAR, a retrieval-augmented diffusion framework that learns market representations by conditioning on similar historical regimes. RADAR leverages retrieval to construct context-dependent noise distributions, applies conditional diffusion to denoise multimodal representations, and initializes the diffusion process using empirical statistics to reflect state-dependent uncertainty. Experiments show that RADAR achieves state-of-the-art performance on key risk-adjusted metrics while producing economically meaningful signals on asset returns and correlations.

Kelvin J. L. Koa, Xinyang Li, Ke-Wei Huang

National University of Singapore Asian Institute of Digital Finance

Portfolio Optimization Stochastic Differential Equations Gaussian Noise Factor

Sep 27, 2026q-fin.PM

Taming the Greeks: Option Portfolios with Inductive Biases

We present an end-to-end deep learning framework for systematic options trading that directly embeds hedging behavior through explicit control of portfolio-level risk exposures. While neural networks trained to optimize risk-adjusted performance have been shown to outperform traditional rules-based strategies, such approaches remain agnostic to the sensitivities of the resulting portfolios with respect to specific underlying risk factors. We propose a general training objective that combines a performance-driven loss with a differentiable risk-sensitivity penalty, enforcing neutrality to selected risk dimensions. Unlike reinforcement learning methods that approximate optimal hedging policies via simulated market dynamics, our framework operates entirely on historical data and jointly optimizes risk-adjusted returns and targeted risk constraints in a single learning problem. We instantiate the framework on static delta-neutral straddle portfolios with the penalty directed at first-order directional exposure, and evaluate two penalty variants -- an exposure-normalized penalty and a Greek-ratio drift penalty. Empirical results on Nasdaq 100 equity options demonstrate that appropriately calibrated regularization simultaneously improves out-of-sample risk-adjusted performance relative to an unregularized baseline while reducing realized directional exposure.

Wee Ling Tan, Stephen Roberts, Stefan Zohren

Department of Engineering Science Oxford-Man Institute of Quantitative Finance University of Oxford

Portfolio Optimization Portfolio Construction Differentiable Optimization Inductive Bias Deep Learning Framework Greek

Sep 15, 2026cs.NE

LLMDE: A Large Language Model-Driven Differential Evolution Algorithm for Portfolio Optimization

This study proposes a Large Language Model-Driven Differential Evolution (LLMDE) algorithm to reduce the reliance on handcrafted hyperparameter design. The proposed algorithm leverages a prompt engineering strategy, allowing large language models (LLMs) to dynamically select mutation strategies and configure control parameters guided by optimization feedback, thus enhancing the performance of the DE algorithm. We evaluate the performance of LLMDE on the CEC2022 benchmark suite, comparing it with standard DE and representative metaheuristics. Furthermore, we employ factor analysis and K-means clustering for stock selection, and then apply LLMDE to solve the Conditional Value at Risk (CVaR) portfolio optimization problem using the selected stocks, subject to budget and minimum expected return constraints. Experimental results demonstrate that LLMDE achieves competitive performance on the benchmark suite while continuously generating high-quality solutions for complex constrained optimization tasks. These outcomes successfully demonstrate the viability of embedding LLMs within metaheuristics, paving a promising path toward the design of advanced LLM-assisted optimization techniques.

Rong Chai, Vaclav Snasel, Xiaopeng Wang +2

Faculty of Electrical Engineering and Computer Science, VŠB-Technical University of Ostrava, Ostrava, Czech Republic · Centre for Artificial Intelligence Research and Optimisation, Torrens University Australia, Brisbane, Australia · Digital Health and Applied Technology Assessment, King’s College London, London, UK

Portfolio Optimization Optimization Modeling

Sep 11, 2026math.OC

Sparsity Regularized and Robust Mean Variance Portfolio Selection Under Ellipsoidal Uncertainty

We investigate mean-variance portfolio selection with an

\ell_0

-penalty to promote sparsity in asset allocations. Uncertainty in the mean return vector is incorporated through an ellipsoidal uncertainty set, yielding a robust sparse optimization framework. We characterize the structure of both local and global minimizers and exploit these properties in the risk minimization and return maximization formulations. Building on this structural insight, we develop a branch-and-bound algorithm tailored to the resulting robust sparse portfolio problems, together with a new pruning rule that can discard exponentially many candidate portfolios in a single step. Extensive computational experiments on real market data, together with comparisons against a mixed-integer second-order cone programming solver, demonstrate the effectiveness and competitiveness of the proposed approach.

Deniz Akkaya, Emre Can Yayla, Buse Şen +1

Department of Industrial Engineering, Bilkent University, Ankara, Türkiye · Risk Analytics and Optimization Chair, EPFL, Lausanne, Switzerland

Portfolio Optimization Sparsity Mean

Sep 1, 2026cs.NE

Reinforcement learning to choose optimizers

No single optimization method is uniformly best for all problems, and the most suitable optimizer choice can change during a run. Existing approaches that change optimizer during execution typically predetermine part of the strategy: the portfolio is restricted to one algorithm class, the switch occurs once at a fixed time, or the frequency of decisions is treated as a hyperparameter rather than a learned one. We introduce "Reinforcement Learning to Choose Optimizers", which formulates the optimization algorithm choice as a sequential decision-making problem. At each decision, a recurrent policy reads the current run state and decides both which optimizer should be used next and for how long. The portfolio includes both gradient-based and derivative-free optimizers, and each switch passes on the current best solution and a representative step size. A context proxy conditions a gating network over expert heads, and training employs a decoupled actor-critic whose return is expressed in the same empirical runtime distribution metric used at evaluation. Training tasks and portfolio are designed jointly so that no optimizer dominates. On unseen problems, the learned policy outperforms every portfolio optimizer at all but the smallest budgets, and it remains robust under distribution shift.

Martin van der Schelling, Deepesh Toshniwal, Miguel A. Bessa

Department of Mechanical Engineering Delft University of Technology, Delft, the Netherlands · Institute of Applied Mathematics Delft University of Technology, Delft, the Netherlands · School of Engineering Brown University, Providence, RI, USA

Portfolio Optimization Sequential Decision Making Differentiable Optimization

Aug 31, 2026q-fin.PM

End-to-End Neural Shrinkage of Indefinite Pairwise Correlation Matrices for Small-Cap-Inclusive Portfolios

Small-cap-inclusive equity universes contain recently listed and intermittently traded securities, so enforcing a common look-back discards a substantial fraction of the available information. Pairwise-complete estimation preserves the longest overlap for each asset pair, but the resulting correlation matrix can be indefinite because its entries are computed on different samples. This prevents direct use in Markowitz optimization and falls outside the assumptions of standard random-matrix shrinkage. We adapt a rotation-invariant neural covariance estimator to this setting. The model computes mask-aware marginal moments and a pairwise correlation matrix proxy, processes its signed spectrum, and uses a bidirectional gated recurrent unit conditioned on factor-aligned effective sample lengths derived from the overlap matrix and eigenvector loadings. It maps all eigenvalues, including negative ones, to a positive inverse spectrum. The reconstructed covariance is positive definite and is trained end-to-end to minimize five-day realized global-minimum-variance risk. We evaluate 26 expanding-window models from 2000 to 2025 on up to 1,500 U.S. equities in a closing-auction simulator with point-in-time selection, commissions, financing, corporate actions, and market impact. Across the 26-year out-of-sample period, the neural estimator reduces annualized five-day volatility by approximately 20% and increases the Sharpe ratio by approximately 40% relative to the next-best covariance estimator. These improvements are consistent across realized risk, risk-adjusted performance, and drawdown control, remain after the modeled execution frictions, and are supported by a 99.9% Model Confidence Set that retains only the neural estimator.

Christian Bongiorno, Lorenzo Villassero

Université Paris-Saclay, CentraleSupélec · Mathématiques et Informatique pour la Complexité et les Systèmes · Gif-sur-Yvette, France +2

Covariance Full-Rank Correlation Matrices Portfolio Optimization Portfolio Construction

Aug 13, 2026cs.LG

Learning Discrete Decisions for MIPs with Constraint-Aware Diffusion

This paper proposes a novel learning-based approach to approximately solve instances of mixed-integer optimization problems. These problems are computationally challenging, as they require jointly determining discrete and continuous decisions while satisfying complex combinatorial constraints. The proposed method relies on a graph-based generative diffusion model that learns the discrete component of mixed-integer optimization problems while integrating a training-free feasibility projection operator directly into the reverse diffusion process to steer intermediate samples toward the feasible set throughout generation. Once the discrete decisions are generated, the remaining optimization reduces to a continuous problem that can be solved efficiently (relative to the original problem) using existing numerical methods. The resulting framework named Constrained Graph Diffusion (CGD), is problem-agnostic and can accommodate a broad class of mixed-integer optimization problems through suitable projection operators. We evaluate CGD on optimal transmission switching for ACOPF and discrete portfolio optimization, demonstrating substantial improvements in feasibility and solution quality over learning-based baselines while achieving speedups of up to

425\times

over state-of-the-art numerical solvers for MINLPs.

Vincenzo Di Vito, Mehdi Taghizadeh, Deepjyoti Deka +2

University of Virginia · MIT · Los Alamos National Laboratory

Mixed-Integer Programming Constrained Optimization Physics-Guided Diffusion Portfolio Optimization Sequential Decision Making Decisions

Aug 7, 2026stat.ML

Optimized Certainty Equivalent Risk Minimization Using Samples: Algorithms, Convergence Rates, and Applications

We consider the optimization of the Optimized Certainty Equivalent (OCE) risk, with applications including portfolio optimization in finance, and uncertainty quantification, classification, and regression in machine learning. Our contributions cover popular special cases of OCE, such as entropic risk, mean-variance risk, and smooth variants of Conditional Value-at-Risk. Our treatment sets out the conditions that facilitate the extension of OCE to unbounded r.v.s.. We provide a useful characterization of OCE that links OCE to utility-based shortfall risk (UBSR). Our characterization enables us to form an OCE estimator from the classic sample-average approximation (SAA) of UBSR. We derive mean-squared error (MSE) bounds for our proposed OCE estimator. For OCE optimization, we first derive an expression for the OCE gradient using the characterization linking OCE to UBSR. This expression serves as the basis for a gradient estimator for the OCE. We derive non-asymptotic bounds on the MSE for the proposed OCE gradient estimator. We incorporate the aforementioned gradient estimator into a stochastic gradient (SG) algorithm to optimize OCE and quantify its convergence rate using non-asymptotic bounds that we derive. Finally, we present three experiments that use our OCE optimization algorithm to solve portfolio optimization and uncertainty quantification problems.

Sumedh Gupte, Prashanth L. A., Sanjay P. Bhat

TCS Research, IIIT-H Research Park, Hyderabad, 500032, India · Department of Computer Science and Engineering, Indian Institute of Technology Madras, Chennai, 600036, India

Portfolio Optimization Stochastic Optimization Conformal Risk Control Stochastic Gradient Descent Convergence

Jul 25, 2026q-fin.PM

Neural Network-Driven Volatility Drag Mitigation under Aggressive Leverage

This paper introduces a compact reformulation of a modular end-to-end neural network for global minimum-variance portfolio optimization that decouples model complexity from both look-back window length and universe size. A five-parameter hyperbolic weighted moving average combined with a saturating exponential replaces the original 2,400-parameter lag-transformation layer, and a bidirectional gated-recurrent-unit eigencleaning module together with a streamlined marginal-volatility network reduce total learnable parameters from 39,586 to just 2,175. In out-of-sample tests against state-of-the-art nonlinear-shrinkage and risk-parity benchmarks, the compact network attains the lowest realized portfolio variance without compromising expected return. Under long-only constraints, the variance reduction supports substantially higher leverage while maintaining comparable drawdown control. Validation in a high-fidelity trading simulator that incorporates realistic margin-call dynamics confirms enhanced over-leverage resilience. These findings demonstrate that end-to-end variance-minimization architectures can achieve substantial parameter efficiency and robust capital-efficiency gains without sacrificing risk-adjusted performance.

Christian Bongiorno, Efstratios Manolakis, Rosario Nunzio Mantegna

Université Paris-Saclay, CentraleSupélec, Mathématiques et Informatique pour la Complexité et les Systèmes, 91190, Gif-sur-Yvette, France · Dipartimento di Fisica e Astronomia “Ettore Majorana” Catania, Italy · Dipartimento di Fisica e Chimica Palermo, Italy +1

Volatility Portfolio Optimization Equivariant Neural Networks Resilience

Jul 10, 2026cs.CE

Large-Scale Portfolio Optimization Problem Under Cardinality Constraint With Enhanced Multi-Objective Evolutionary Algorithms

Decision-making is posing an increasingly formidable challenge to investors because of the growing number of alternatives available in financial markets. A hot area of research over the past few decades has been portfolio optimization that seeks to determine how much an investor should invest in which asset. Introducing real-world conditions to the optimization model turns the problem into an NP-hard one for whose solution exact methods become inefficient; hence, researchers have turned to evolutionary algorithms to approximate solutions. In this paper, strengthening strategies are presented for multi-objective evolutionary algorithms that can provide a faster convergence rate and extensive search ability in the portfolio optimization problem under the cardinality constraint. To implement those features, a unique solution representation, a novel operator, and new repair mechanisms are introduced for solving the aforementioned problem in which lower and upper limits are set on the number of assets in the portfolio. For this purpose, new mating strategies along with the aforesaid package are implemented in well-known multi-objective evolutionary algorithms to solve the problem. The customized algorithms are subsequently tested against traditional ones using well-known market indices as benchmarks. Results indicate that the proposed strategy not only provides better approximations but also converges faster as well at no loss of performance with an increasing number of assets in the market.

Danial Ramezani, Mostafa Abouei Ardakan

Department of Industrial Engineering, Faculty of Engineering, Kharazmi University, Tehran, Iran

Portfolio Optimization Multi-Objective Optimization Cardinality

Jul 10, 2026cs.LG

Learning Predictive Ambiguity Sets for Decision-Focused Distributionally Robust Optimization

Predict-then-optimize systems usually compress uncertainty into a point forecast and then solve a downstream optimization problem as if the forecast were reliable. Distributionally robust optimization (DRO) offers protection against misspecification, but the ambiguity set is often centered at historical samples and uses a fixed radius. We propose \emph{learned predictive ambiguity sets} (LPAS): a deep contextual model outputs a finite nominal scenario distribution, a state-dependent Wasserstein radius, and optionally an anisotropic ground metric. These outputs define a contextual ambiguity set that feeds a DRO decision layer. The radius is trained by a combination of conditional quantile calibration, size regularization, and downstream decision loss, so that robustness is adaptive rather than globally fixed. We derive the finite dual form used by the decision layer, present a staged training algorithm, and evaluate the method on distributionally robust portfolio optimization with 20 S&P 500 constituents from 2018--2026. The proposed method substantially improves over equal-weight, predict-then-optimize, and historical Wasserstein DRO baselines, achieving 26.28% annualized return, Sharpe ratio 1.30, final wealth 1.61, and lower tail loss than a deep fixed-radius DRO baseline while using a smaller average radius. The results show that learned ambiguity radii can recover most of the performance of strong fixed-radius DRO while reducing unnecessary conservatism and improving regime adaptivity.

Junjie Guo

Rutgers University

Distributionally-Robust Optimization Robust Optimization Portfolio Optimization Predictive Uncertainty Wasserstein Distance Ambiguity

Jul 7, 2026cs.LG

Deep Reinforcement Learning for Reliability Based Bi-Objective Portfolio Optimization

Portfolio optimization under uncertainty is inherently a multi-objective decision problem involving complex interactions among return, risk, market dynamics, and practical investment constraints. Existing reliability based portfolio optimization approaches primarily rely on static optimization frameworks and often fail to capture sequential decision making, tail risk, and market frictions such as transaction costs. To address these limitations, we propose a deep reinforcement learning framework for multi-objective reliability based portfolio optimization (MORP-DRL). The proposed framework jointly optimizes expected return and downside risk using three complementary risk measures: variance, Conditional Value-at-Risk (CVaR), and Entropic Value-at-Risk (EVaR). To model uncertainty and heavy-tailed market behavior, asset returns are represented using GARCH(1,1), Extreme Value Theory, and a t-copula dependence structure, while realistic scenarios are generated through quasi-Monte Carlo simulation. A Proximal Policy Optimization (PPO) based strategy is developed under practical constraints including transaction costs and portfolio bounds, and is benchmarked against NSGA-II. Experiments on ten global equity indices across pre-COVID, COVID, and post-COVID market regimes demonstrate that MORP-DRL achieves competitive risk-return performance, reduced downside risk during periods of market stress, and scalability to high-dimensional portfolio settings.

Sounaq Das, Tanmay Sen, Raghu Nandan Sengupta +1

Indian Institute of Management Amritsar · Amritsar, India · SQC & OR Unit +7

Portfolio Optimization Conditional-Value-At-Risk Multi-Objective Reinforcement Learning

Jul 1, 2026cs.LG

Decision-focused Sparse Tangent Portfolio Optimization

Sparse tangent portfolio optimization aims to learn an interpretable, low-cardinality portfolio in the tangency direction of the mean-variance frontier. However, the associated cardinality-constrained formulation is NP-hard, and standard predict-then-optimize pipelines often misalign forecasting accuracy with downstream portfolio quality. We propose an end-to-end decision-focused learning framework that reformulates Sharpe ratio maximization as a Disciplined Parametrized Programming (DPP)-compliant convex programming layer and replaces discrete selection with a smooth top-

k

operator enforcing an exact cardinality

k

. This enables gradient flow through prediction, asset selection, and re-optimization, allowing the predictive model to directly optimize portfolio performance. Across four major equity markets, our method achieves competitive and often superior out-of-sample Sharpe ratios compared with historical and prediction-focused baselines, with particularly strong gains in larger asset universes. Our \href{https://github.com/feuerwerksh/Diffble-card-SR}{code} is publicly available.

Haeun Jeon, Seunghoon Choi, Hyunglip Bae +2

Department of Industrial and Systems Engineering, Korea Advanced Institute of Science and Technology, Daejeon, Republic of Korea · Department of Big Data Convergence, and Bigdata Research Lab, Chonnam National University, Gwangju, Republic of Korea · Department of Industrial Engineering, Ulsan National Institute of Science and Technology, Ulsan, Republic of Korea

Portfolio Optimization Pareto Frontier Cardinality

Jun 25, 2026stat.ML

The Decision Geometry of Covariance Estimation for the Global Minimum-Variance Portfolio under Heavy Tails

The global minimum-variance portfolio (GMVP) is the canonical decision built from an estimated covariance matrix, yet covariance estimators are universally evaluated by matrix-norm loss, which is not the object the decision depends on. We characterise exactly how covariance-estimation error maps into GMVP suboptimality. We prove an exact regret identity and a non-asymptotic bound showing decision regret depends on the estimation error only through its action on the portfolio weights, scaled by portfolio concentration and the conditioning of the true covariance. From this we derive the decision geometry: GMVP regret is invariant to a (p-1)-dimensional projection of the p^2-dimensional error matrix, with invariance to the covariance-scale direction as an exact special case. We then apply the framework to heavy-tailed returns (tail index kappa in (2,4)), establishing the regret convergence rate implied by the centred operator-norm rate, and confirm the theory on a skew-t/t-copula simulation design with pre-registered analysis. The decision-focused advantage is a sharper constant and a concentration discount rather than a faster rate; we report an honest high-conditioning boundary of the rate prediction. The results complement recent decision-focused learning approaches by supplying the exact estimation geometry and consistency theory they lack.

Xavier Fonseca

Academy for AI, Games and Media, Breda University of Applied Sciences, Breda, The Netherlands.

Portfolio Optimization Covariance Long-Tailed Distribution Spectral Norm

Jun 24, 2026math.OC

Generating Input Distributions for Explaining Portfolio Optimization Pipelines

We propose a predict-optimize-explain framework that uses gradient-based sample generation to interpret various portfolio models by identifying macroeconomic conditions that induce specified portfolio outcomes. Unlike traditional feature-importance methods, this approach directly probes decision pipelines (predictive models coupled with portfolio optimization) by constructing economically meaningful what-if questions. We focus on four such questions: under what macroeconomic conditions a predict-then-optimize pipeline closes or reverses its return gap with a predict-and-optimize pipeline; what conditions lead a pipeline to diversify rather than concentrate its allocation; when a pipeline trained on calm markets overtakes one trained through crises; and what conditions would let a pipeline match a benchmark return. These examples illustrate how our framework uncovers key behavioral differences between various decision pipelines. Beyond these cases, the proposed framework is flexible and can support a wide range of probing questions tailored to specific portfolio objectives. Our findings highlight the value of integrating prediction, optimization, and explanation to produce more robust and transparent portfolio strategies.

Batuhan Ataş, Nurşen Aydın, E. Mehmet Kıral +1

Faculty of Economics and Business, University of Amsterdam, The Netherlands · Warwick Business School, University of Warwick, United Kingdom · RIKEN AIP, Japan

Portfolio Optimization Portfolio Construction Economies

Jun 10, 2026q-fin.CP

Deterministic Policy Gradient for Learning Equilibrium in Time-Inconsistent Control Problems

In this paper, we develop a continuous-time model-free reinforcement learning algorithm to learn deterministic equilibrium policies in general time-inconsistent control problems. Utilizing the extended Hamilton-Jacobi-Bellman system, we recast the original time-inconsistent problem into an equivalent two-stage problem. In the first stage, for given auxiliary functions, we employ the deterministic policy gradient approach to learn an optimal policy in an auxiliary time-consistent control problem. In the second stage, given the updated policy, we exploit the inner fixed point iterations and some martingale characterizations to learn the auxiliary functions. As a theoretical contribution, we provide some mild model assumptions and establish the convergence of inner fixed point iterations. By repeating this actor-critic style of iterations across two stages, our algorithm aims to learn the equilibrium under different sources of time-inconsistency in a unified manner. The superior effectiveness of the proposed algorithm are illustrated in two classical financial applications with time-inconsistency: mean-variance portfolio management and optimal tracking portfolio under non-exponential discounting.

Xin Guo, Yijie Huang, Xiang Yu

Department of Industrial Engineering and Operations Research, University of California, Berkeley, USA. · Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong.

Optimal Control Portfolio Optimization Equilibrium

Jun 8, 2026cs.LG

Addressing Market Regime Changes and Heavy-Tailed Returns in Portfolio Optimization via Bayesian VAR and Elliptical Black-Litterman

Deep reinforcement learning (DRL) frameworks for portfolio optimization have shown promise for their ability to learn allocation rules dynamically from market data. However, these models fail to account for fat-tailed returns, which characterize actual market behavior with more frequent extreme events. Furthermore, historical data is treated homogeneously, without accounting for temporal importance, leading models to fail during regime changes. We propose a new BAVAR-BLED algorithm that combines methods derived from Bayesian-Averaging Vector Autoregressive (BAVAR) and the Black-Litterman model using Elliptical Distributions (BLED) within a TD3 architecture. BAVAR captures a set of vector autoregressive representations that consider multi-scale temporal features, enabling adaptive allocation decisions based on regime-aware estimates of return expectations and dispersion matrices. These estimates serve as prior inputs to BLED, a model that uses Student's t-distributions, allowing for more realistic fat tail return estimates. The BAVAR-BLED algorithm uses transformer networks for view construction and CNNs for risk-aversion estimates, which modify dynamic allocation decisions based on market conditions. An evaluation of 29 Dow Jones Industrial Average constituents over a decade-long market period shows that BAVAR-BLED significantly outperforms state-of-the-art methods, achieving Sharpe and Sortino ratios of 1.72 and 2.70, respectively, and total returns of 57.26%.

Daniil Mikriukov, Ruoyu Sun, Angelos Stefanidis +2

University of Liverpool · Xi'an Jiaotong-Liverpool University · Department of Computer Science, University of Liverpool, Liverpool, United Kingdom +1

Portfolio Optimization Long-Tailed Distribution Maximum Likelihood Autoregressive Model Visual Autoregressive Models

Jun 7, 2026cs.LG

Scaling Decision-Focused Learning to Large Problems with Lagrangian Decomposition

Decision-focused learning has shown great promise for addressing predict-then-optimize problems, particularly in the presence of under-specified models. However, its practical deployment is often hindered by high computational costs and limited scalability, as it requires solving a constrained optimization problem for each training instance at every iteration. To address these challenges, we propose a novel framework that incorporates Lagrangian decomposition into the decision-focused learning paradigm. Specifically, we introduce a new surrogate objective along with two loss functions for evaluating and training the underlying prediction model. We further propose two variants of our approach, which offer different trade-offs between computational efficiency and solution quality. Our framework can be seamlessly integrated with standard decision-focused learning methods, including Smart Predict-then-Optimize (SPO+) and Implicit Maximum Likelihood Estimation (IMLE). Through experiments on two standard benchmarks, the multi-dimensional knapsack problem and quadratic portfolio optimization, we demonstrate that our approach achieves competitive performance while remaining amenable to parallelization. In particular, it consistently outperforms traditional decision-focused learning methods on large-scale instances, involving up to eight times more variables than those typically considered in related work. The implementation is available at https://github.com/corail-research/DFL-LD.

Stéphane Eilles-Chan Way, Hugo Percot, Quentin Cappart +2

Polytechnique Montréal, Montreal, Canada · Ecole Polytechnique, Palaiseau, France · UCLouvain, Louvain-la-Neuve, Belgium +2

Linear Programming Decentralized Optimization Portfolio Optimization Decomposition Lagrangian Methods Scaling

Jun 4, 2026cs.LG

Diffusion Models for Adaptive Sequential Data Generation

Generating realistic synthetic sequential data is critical in real-world applications across operations research, finance, healthcare, energy systems, and scientific computing, where time-indexed observations are used for prediction, simulation, risk assessment, and data-driven decision-making. While diffusion models have achieved remarkable success in generating static data, their direct extensions to sequential settings often fail to capture temporal dependence and information structure. Designing diffusion models that can simulate sequential data in an adapted manner, and hence without anticipation of future information, therefore remains an open challenge. In this work, we propose a sequential forward-backward diffusion framework for adapted time series generation. Our approach progressively injects and removes noise along the sequence, conditioning on the previously generated history to ensure adaptiveness. A novel score-matching objective is introduced for efficient parallel training. We derive rigorous statistical guarantees under a generic framework, then establish score approximation, score estimation, and distribution estimation results with ReLU networks serving as a concrete instance. Empirically, we validate our method on synthetic data, including ARMA models and Gaussian processes, and demonstrate its effectiveness in constructing mean-variance optimal portfolios.

Haoyang Cao, Minshuo Chen, Yinbin Han +1

Department of Applied Mathematics and Statistics, Data Science and AI Institute, and Mathematical Institute for Data Science, Johns Hopkins University. · Department of Industrial Engineering and Management Sciences, Northwestern University. · Department Management Science and Engineering, Stanford University.

Time-Series Generation Diffusion Models Synthetic Data Sequential Portfolio Optimization Temporal Dependence

May 26, 2026cs.AI

Generating Robust Portfolios of Optimization Models using Large Language Models

Mathematical optimization is a powerful tool for structured decision-making across domains such as resource allocation and planning. Formulating optimization models faithful to reality, though, remains a significant bottleneck as it typically demands both domain expertise and optimization knowledge that are often scarce. Recent advances in large language models (LLMs) promise to bridge this gap, enabling the generation of candidate optimization models from natural language descriptions. However, there is no guarantee that any single LLM-generated model is reliable, and existing approaches that output only one model are therefore risky. In this work, we propose a novel algorithm that generates a portfolio of optimization models, designed to be robust to the limitations of LLMs. Our method exploits the observation that a single LLM can play two distinct roles

\unicode{x2014}

as a stochastic generator and as a reasoning evaluator

\unicode{x2014}

and proposes a unified framework that leverages both capabilities in a complementary manner. We provide theoretical guarantees showing that, as long as either the generator or the evaluator is well-aligned with human preferences, the portfolio is guaranteed to contain high-quality candidates, enabling a principled human-in-the-loop process in which a decision-maker can review multiple candidates before committing to one. We further validate our approach empirically, demonstrating strong performance across a range of optimization modeling tasks.

Eleni Straitouri, Cheol Woo Kim, Milind Tambe

Max Planck Institute for Software Systems, Kaiserslautern, Germany · Harvard University, Cambridge, United States

Optimization Modeling Portfolio Optimization

May 25, 2026cs.MA

Recursive Multi-Agent Trading System: Iterative Optimized Portfolio Strategy Under Geopolitical Uncertainty

Recursive Multi-Agent Trading System (RMATS) integrates four specialized agents -- Sentiment, Report, Analysis, and Risk -- coordinated through a recursive Manager Agent with iterative feedback loops. Experimental evaluation over a 561-trading-day period (January 2023 to March 2025) across a 24-asset multi-class universe demonstrates that RMATS achieves a maximum drawdown of 9.62%, lower than MVO (15.49%) and FinBERT Sentiment (15.28%), and exhibits the lowest event-period drawdown in 3 of 5 geopolitical stress scenarios tested. While RMATS underperforms return-maximizing baselines in a sustained bull market environment, ablation studies confirm the individual contribution of each agent component to downside protection. These results position RMATS as a risk-control-oriented architecture suitable for institutions prioritizing capital preservation under geopolitical uncertainty.

Jing Yang, Yichao Wu, Jianan Liu +4

Washington University in St. Louis · Northeastern University · Independent Researcher +1

Model-Based Multi-Agent Systems Portfolio Optimization Geopolitical Grounding Interacts Matching Markets Uncertainty

May 23, 2026stat.ML

Clustering based on Stochastic Dominance with application for risk averters and risk seekers

Stochastic Dominance (SD) theory provides a rigorous framework for selecting superior assets tailored to the asset allocation needs of investors with varying risk preferences (i.e., risk-averse, risk-seeking, and risk-neutral). However, traditional stock clustering methods typically rely on geometric metrics such as Euclidean distance, which often fail to effectively capture the intrinsic risk dominance relationships among assets. To address this limitation, this paper proposes an innovative clustering analysis framework based on SD test statistics. Methodologically, this study deeply integrates SD theory with machine learning algorithms. Transcending the limitations of traditional reliance on geometric distance, we innovatively utilize test statistics from first-, second-, and third-order SD to construct a "Stochastic Dominance Coefficient Matrix." Building upon this matrix, we modify the classic K-means and Hierarchical Clustering algorithms. Specifically, we derive 12 distinct algorithm variants tailored to different orders of SD relationships. Simultaneously, we construct the SD-SC coefficient and the SD-DBI index as specialized validity indices to evaluate the clustering performance. Empirically, we analyze constituent stock data from a representative developed market (the US NASDAQ Index) and an emerging market (China's CSI 100 Index). The results verify the effectiveness and robustness of the proposed method. Furthermore, we apply the clustering results to the modification of the Single Index Model and the construction of Global Minimum Variance Portfolios (GMVP). The findings demonstrate that the proposed method effectively facilitates customized asset allocation for investors, holding significant theoretical value and practical implications.

Hua Li, Xue Jia, Yilin Kang +1

School of Science, Changchun University, Changchun, China. · School of Mathematics and Science, Northeast Normal University, Changchun, China.

Portfolio Optimization Clustering Portfolio Construction Risk

May 16, 2026q-fin.PM

Financially Guided Deep Portfolio Optimization

Portfolio optimization in real-world financial markets is notoriously difficult due to non-stationarity, noisy data, and high transaction costs. Standard predict-then-optimize methods first forecast returns and then solve for weights, compounding prediction errors and often failing under regime shifts. We propose an end-to-end framework that directly optimizes differentiable surrogates of key financial metrics (Sharpe ratio, Omega ratio, Conditional Value-at-Risk, and risk parity), allowing neural networks to learn portfolio weights via backpropagation. Our expanding-window walk-forward procedure, applied to 50 S&P 500 stocks from 2007 to 2023, incorporates realistic bid-ask spread costs and rebalances quarterly. On the challenging out-of-sample test period (2022-2023), the best model, an AttentionLSTM with the Omega-CVaR-RiskParity loss, achieves an annualized Sharpe of 0.29 and a total compounded return of +7.86%, while the S&P 500 delivers -4.52% total compounded return and an annualized Sharpe of -0.02. This outperforms the S&P 500 by 12.38 percentage points, while keeping tail risk (CVaR) nearly unchanged. The framework outperforms the equal-weight portfolio, S&P 500, and traditional methods (MVP, HRP, NCO, ERC), demonstrating that embedding financial objectives directly into model training yields robust, economically meaningful outperformance even in adverse market conditions.

Rahul Fernandes, Travis Desell

Department of Software Engineering Rochester Institute of Technology Rochester, New York, USA

Portfolio Optimization Portfolio Construction Conditional-Value-At-Risk

May 13, 2026econ.EM

Regret Equals Covariance: A Closed-Form Characterization for Stochastic Optimization

Regret is the cost of uncertainty in algorithmic decision-making. Quantifying regret typically requires computationally expensive simulation via Sample Average Approximation (SAA), with complexity

\mathcal{O}(Bn^{2}d^{3})

in the number of scenarios

B

, variables

n

, and constraints

d

. % This paper proves that expected regret in any stochastic optimization problem admits the exact decomposition % \begin{equation*} \mathrm{Regret}(c) = \mathrm{Cov}(c,,π^{}(c)) + R(c), \end{equation} % where

c

is the vector of uncertain parameters,

π^{*}(c)

is the optimal decision, and

R(c)

is a residual whose magnitude we bound explicitly under Lipschitz, smooth, and strongly convex conditions. % For linear programs and unconstrained quadratic programs, including the classical Markowitz portfolio problem, we prove

R(c)=0

exactly, so that

\mathrm{Regret}(c) = \mathrm{Cov}(c,π^{*}(c))

holds without approximation. % When historical cost-decision pairs

\{(c_i, π^*(c_i))\}

are available, the covariance can be estimated in

\mathcal{O}(nd^{2})

time, which is orders of magnitude faster than SAA. The estimation is performed by a single pass through the data. % We derive concentration bounds, a central limit theorem, and an asymptotically unbiased residual estimator, and we validate all results on synthetic LP, QP, and integer programming instances and on a rolling-window portfolio experiment using ten years of CRSP equity data.

Irene Aldridge

Optimal Regret Regret Portfolio Optimization Stochastic Optimization Covariance Quadratic Programs+1

May 10, 2026cs.AI

Beyond ESG Scores: Learning Dynamic Constraints for Sequential Portfolio Optimization

ESG-aware portfolio optimization is increasingly important for sustainable capital allocation, yet most learning-based methods still operationalize ESG by appending static scores to the policy observation or reward. This creates a mismatch for sequential control: ESG scores are noisy, provider-dependent, low-frequency, and temporally misaligned with sequential portfolio decisions, while financial evidence suggests that ESG is better treated as a portfolio preference, risk-exposure, or hedge dimension than as a robust alpha factor. We propose to impose ESG constraints without modifying the financial policy's observation or reward, using a Multimodal Action-Conditioned Constraint Field (MACF) that learns mechanism-specific ESG costs from point-in-time multimodal evidence and contemplated portfolio transitions. We then introduce MACF-X, a family of optimizer-specific adapters that converts MACF costs and uncertainties into native constrained-optimization interfaces through a shared slack- and uncertainty-aware pressure layer. Across multiple constraint-integration interfaces, MACF-X reduces tail ESG budget pressure while maintaining competitive financial performance. Ablations show that this improvement depends on dynamic evidence inputs and three-head decomposition, while static ESG-score proxies are nearly indistinguishable from score-shuffled noise baselines.

Xin Li, Yan Ke, Longbing Cao

Macquarie University · The University of Queensland

Portfolio Optimization Portfolio Construction Structural Constraints

May 4, 2026cs.LG

A Meta Reinforcement Learning Approach to Goals-Based Wealth Management

Applying concepts related to zero-shot meta-learning and pre-training of foundation models, we develop a meta reinforcement learning approach (denoted MetaRL) that is pre-trained on thousands of goals-based wealth management (GBWM) problems. Each GBWM problem involves a multiple year scenario over which the investor looks to optimally choose an investment portfolio each year and choose to fulfill all, some, or none of the different financial goals that arise each year. These choices seek to maximize the expected total investor utility obtained from the fulfilled financial goals. By eliminating separate training and optimization for each new investor problem, the MetaRL model in inference mode produces near-optimal dynamic investment portfolio and goal-fulfilling strategies for a new GBWM problem within a few hundredths of a second. This delivers expected utilities that are, on average, 97.8% of the optimal expected utilities (determined via Dynamic Programming). These results are remarkably robust to capital market regime changes, even when training uses only one capital market regime. Further, the MetaRL approach can enable solving problems with larger state spaces where Dynamic Programming becomes computationally infeasible.

Sanjiv R. Das, Harshad Khadilkar, Sukrit Mittal +3

Dept. of Finance, Santa Clara University, Santa Clara, CA, USA · Indian Institute of Technology, Mumbai, India · Franklin Templeton, Mumbai, India +4

Portfolio Optimization Offline Reinforcement Learning

Apr 30, 2026math.OC

Sampler-Robust Optimization under Generative Models

Modern stochastic optimization pipelines increasingly rely on learned generative models to represent uncertainty, while downstream decisions are evaluated almost entirely through Monte Carlo scenarios. This shifts the operational object of uncertainty from an explicit probability law to the sampler induced by the learned generator. Reliability therefore depends on two errors: sampler misspecification and finite-simulation error. We propose Sampler-Robust Optimization (SRO), which optimizes decisions against the worst-case sampler induced by perturbing the learned generator. This sampler-first formulation aligns with simulation-based decision pipelines and admits a sharpness-aware interpretation: it favors decisions whose performance is stable under generator perturbations, rather than merely under the nominal sampler. Under a coverage assumption, we show that the empirical worst-case objective provides a high-probability upper certificate for the true population objective, with finite-simulation error partially absorbed by the robustification used to guard against sampler misspecification. The framework accommodates generative models with or without explicit densities and admits efficient minimax procedures. Portfolio-optimization experiments show that SRO produces more stable decisions and improves out-of-sample performance under distribution shift.

Ziwei Zhang, Jonathan Yu-Meng Li

Telfer School of Management University of Ottawa

Robust Optimization Portfolio Optimization Generative Models

Apr 20, 2026cs.NE

Similarity-based Portfolio Construction for Black-box Optimization

In black-box optimization, a central question is which algorithm to use to solve a given, previously unseen, problem. Selecting a single algorithm, however, entails inherent risks: inaccuracies in the selector may lead to poor choices, and even well-performing algorithms with high variance can yield unsatisfactory results in a single run. A natural remedy is to split the evaluation budget across multiple runs of potentially different algorithms. Such sequential algorithm portfolios benefit from variance reduction and complementarities between algorithms, often outperforming approaches that allocate the entire budget to a single solver. While effective portfolios can be constructed post-hoc, transferring this idea to the algorithm selection setting is non-trivial. We show that a naive portfolio constructed over the full training set already outperforms the strongest traditional baseline, the virtual best solver. We then propose a simple yet effective k-nearest-neighbor-based finetuning approach to construct portfolios tailored to unseen instances, yielding further improvements and highlighting the effectiveness of portfolio selection in fixed-budget black-box optimization.

Catalin-Viorel Dinu, Diederick Vermetten, Carola Doerr

Sorbonne Université, CNRS, LIP6

Black-Box Optimization Algorithm Selection Portfolio Optimization Portfolio Construction Functional Code Solvers Variance Reduction+1

Apr 18, 2026q-fin.GN

The Virtue of Sparsity in Complexity

Sparsity or complexity? In modern high-dimensional asset pricing, these are often viewed as competing principles: recent empirical evidence favors richer models, while economic intuition has long favored parsimony. We reconcile this tension by distinguishing capacity sparsity-restrictions on effective model capacity-from factor sparsity-the parsimonious structure of priced risks. Revisiting the benchmark empirical design of Didisheim et al. (2025), we combine nonlinear feature expansions with basis pursuit, using column generation and GPU acceleration to scale estimation to 432 million candidate factors. Reaching this scale reveals a reversal in out-of-sample performance: sparse portfolios trail dense ridgeless benchmarks at lower complexity but achieve a higher Sharpe ratio and lower pricing error at the largest candidate set. Capacity expansion and factor sparsity are therefore complements: enlarging the candidate space allows a parsimonious pricing kernel to outperform its dense counterpart.

Nima Afsharhajari, Jonathan Yu-Meng Li

Telfer School of Management University of Ottawa

Portfolio Optimization Sparsity Exploratory Factor Analysis Economies Ethics

Dec 17, 2025cs.LG

Adaptive Partitioning and Learning for Stochastic Control of Diffusion Processes

We study reinforcement learning for controlled diffusion processes with unbounded continuous state spaces, bounded continuous actions, and polynomially growing rewards: settings that arise naturally in finance, economics, and operations research. To overcome the challenges of continuous and high-dimensional domains, we introduce a model-based algorithm that adaptively partitions the joint state-action space. The algorithm maintains estimators of drift, volatility, and rewards within each partition, refining the discretization whenever estimation bias exceeds statistical confidence. This adaptive scheme balances exploration and approximation, enabling efficient learning in unbounded domains. Our analysis establishes regret bounds that depend on the problem horizon, state dimension, reward growth order, and a newly defined notion of zooming dimension tailored to unbounded diffusion processes. The bounds recover existing results for bounded settings as a special case, while extending theoretical guarantees to a broader class of diffusion-type problems. Finally, we validate the effectiveness of our approach through numerical experiments, including applications to high-dimensional problems such as multi-asset mean-variance portfolio selection.

Hanqing Jin, Renyuan Xu, Yanzhao Yang

Mathematical Institute, University of Oxford · Department of Management Science and Engineering, Stanford University

Stochastic Optimal Control Distributional Reinforcement Learning Portfolio Optimization Partitioning Regret High-Dimensional

Dec 12, 2025cs.CE

Integrated Prediction and Multi-period Portfolio Optimization

Multi-period portfolio optimization is important for real portfolio management, as it accounts for transaction costs, path-dependent risks, and the intertemporal structure of trading decisions that single-period models cannot capture. Classical methods usually follow a two-stage framework: machine learning algorithms are employed to produce forecasts that closely fit the realized returns, and the predicted values are then used in a downstream portfolio optimization problem to determine the asset weights. This separation leads to a fundamental misalignment between predictions and decision outcomes, while also ignoring the impact of transaction costs. To bridge this gap, recent studies have proposed the idea of end-to-end learning, integrating the two stages into a single pipeline. This paper introduces IPMO (Integrated Prediction and Multi-period Portfolio Optimization), a model for multi-period mean-variance portfolio optimization with turnover penalties. The predictor generates multi-period return forecasts that parameterize a differentiable convex optimization layer, which in turn drives learning via portfolio performance. For scalability, we introduce a mirror-descent fixed-point (MDFP) differentiation scheme that avoids factorizing the Karush-Kuhn-Tucker (KKT) systems, which thus yields stable implicit gradients and nearly scale-insensitive runtime as the decision horizon grows. In experiments with real market data and two representative time-series prediction models, the IPMO method consistently outperforms the two-stage benchmarks in risk-adjusted performance net of transaction costs and achieves more coherent allocation paths. Our results show that integrating machine learning prediction with optimization in the multi-period setting improves financial outcomes and remains computationally tractable.

Yuxuan Linghu, Zhiyuan Liu, Qi Deng

Georgia Institute of Technology · The University of Chicago · Shanghai Jiao Tong University

Portfolio Optimization Multivariate Time Series Forecasting Horizon