arXiv subjects

Grani A. Hanasusanto

Publications and source records attributed to Grani A. Hanasusanto.

At least 19 recordsLinked to original sources

arXiv2026

Data-Driven Contextual Optimization with Gaussian Mixtures: Flow-Based Generalization, Robust Models, and Multistage Extensions

Contextual optimization enhances decision quality by leveraging side information to improve predictions of uncertain parameters. However, existing approaches face significant challenges when dealing with multimodal or mixtures of distributions. The inherent complexity of such structures often precludes an explicit functional relationship between the contextual information and the uncertain parameters, limiting the direct applicability of parametric models. Conversely, while non-parametric models offer greater representational flexibility, they are plagued by the "curse of dimensionality," leading to unsatisfactory performance in high-dimensional problems. To address these challenges, this paper proposes a novel contextual optimization framework based on Gaussian Mixture Models (GMMs). This model naturally bridges the gap between parametric and non-parametric approaches, inheriting the favorable sample complexity of parametric models while retaining the expressiveness of non-parametric schemes. By employing normalizing flows, we further relax the GM assumption and extend our framework to arbitrary distributions. Finally, inspired by the structural properties of GMMs, we design a novel GMM-based solution scheme for multistage stochastic optimization problems with Markovian uncertainty. This method exhibits significantly better sample complexity compared to traditional approaches, offering a powerful methodology for solving long-horizon, high-dimensional multistage problems. We demonstrate the effectiveness of our framework through extensive numerical experiments on a series of operations management problems. The results show that our proposed approach consistently outperforms state-of-the-art methods, underscoring its practical value for complex decision-making problems under uncertainty.

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arXiv2026

Distributionally Robust Optimization via Targeted Integral Probability Metrics for General Data Processes

Distributionally robust optimization (DRO) provides a principled framework for decision-making under distributional uncertainty. Classical data-driven DRO frameworks typically construct ambiguity sets from distributional information, such as moment constraints, divergence neighborhoods, or Wasserstein balls, specified before the downstream loss is considered. We propose a task-aware DRO framework based on targeted integral probability metrics. The ambiguity set is defined directly through the loss functions induced by feasible decisions, thereby controlling the loss discrepancy between an adversarial distribution and a data-driven reference distribution. This construction leads to an expected hinge-constrained formulation that is equivalent to an infinitely constrained loss-discrepancy formulation. It also yields finite-sample guarantees that bypass the ambient curse of dimensionality: whenever an appropriate scalar pointwise concentration inequality is available for the induced loss estimator, the ambiguity radius can be calibrated at the canonical $\widetilde{\mathcal O}(N^{-1/2})$ rate after uniformization over the decision class. As a result, the framework applies broadly to settings including heavier-tailed sub-Weibull losses, Markovian data, outlier-corrupted data, and incomplete data. We derive exact infinite-dimensional dual reformulations, establish out-of-sample and excess-risk guarantees, and develop a conservative Monte Carlo approximation scheme with convergence and suboptimality guarantees. For piecewise affine losses, the sampled problems admit tractable conic reformulations. Numerical experiments in inventory management under heavy-tailed demand and regression with outlier corruption demonstrate strong out-of-sample performance relative to existing approaches.

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arXiv2026

DR-SAC: Distributionally Robust Soft Actor-Critic for Reinforcement Learning under Uncertainty

Deep reinforcement learning (RL) has achieved remarkable success, yet its deployment in real-world scenarios is often limited by vulnerability to environmental uncertainties. Distributionally robust RL (DR-RL) algorithms have been proposed to resolve this challenge, but existing approaches are largely restricted to value-based methods in tabular settings. In this work, we introduce Distributionally Robust Soft Actor-Critic (DR-SAC), the first actor-critic based DR-RL algorithm for offline learning in continuous action spaces. DR-SAC maximizes the entropy-regularized rewards against the worst possible transition models within an KL-divergence constrained uncertainty set. We derive the distributionally robust version of the soft policy iteration with a convergence guarantee and incorporate a generative modeling approach to estimate the unknown nominal transition models. Experiment results on five continuous RL tasks demonstrate our algorithm achieves up to 9.8 times higher average reward than the SAC baseline under common perturbations. Additionally, DR-SAC significantly improves computing efficiency and applicability to large-scale problems compared with existing DR-RL algorithms. Code is publicly available at github.com/Lemutisme/DR-SAC.

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arXiv2026

A Distributionally Robust Optimization Approach to Quick Response Models under Demand Uncertainty

Quick response is a widely adopted strategy to mitigate overproduction in the manufacturing industry, yet recent research reveals a counter-intuitive paradox: while it reduces waste from unsold finished goods, it may incentivize firms to procure more raw materials, potentially increasing total system waste. Additionally, existing models that guide quick response strategies rely on the assumption of a known demand distribution, whereas in practice, demand patterns are often ambiguous and historical data are scarce. To address these challenges, we develop a distributionally robust optimization (DRO) framework for the quick response model that builds robust policies even with limited data. We further integrate a novel waste-to-consumption ratio constraint into this framework, empowering firms to explicitly control the environmental impact of their operations. Our numerical experiments demonstrate that policies optimized for specific demand assumptions suffer severe performance degradation under distributional shifts, whereas our data-driven DRO approach consistently delivers superior robustness. Moreover, we find that the constrained quick response model resolves the central paradox: it can achieve higher profits with verifiably less total waste than a traditional, non-flexible alternative. These results resolve the `quick response or not' debate by showing that the question is not \emph{whether} to use quick response, but \emph{how} to manage it. By incorporating socially responsible metrics as constraints, the quick response system delivers a `win-win' outcome for both profitability and the environment compared to traditional systems.

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arXiv2025

Clip-and-Verify: Linear Constraint-Driven Domain Clipping for Accelerating Neural Network Verification

State-of-the-art neural network (NN) verifiers demonstrate that applying the branch-and-bound (BaB) procedure with fast bounding techniques plays a key role in tackling many challenging verification properties. In this work, we introduce the linear constraint-driven clipping framework, a class of scalable and efficient methods designed to enhance the efficacy of NN verifiers. Under this framework, we develop two novel algorithms that efficiently utilize linear constraints to 1) reduce portions of the input space that are either verified or irrelevant to a subproblem in the context of branch-and-bound, and 2) directly improve intermediate bounds throughout the network. The process novelly leverages linear constraints that often arise from bound propagation methods and is general enough to also incorporate constraints from other sources. It efficiently handles linear constraints using a specialized GPU procedure that can scale to large neural networks without the use of expensive external solvers. Our verification procedure, Clip-and-Verify, consistently tightens bounds across multiple benchmarks and can significantly reduce the number of subproblems handled during BaB. We show that our clipping algorithms can be integrated with BaB-based verifiers such as $α,β$-CROWN, utilizing either the split constraints in activation-space BaB or the output constraints that denote the unverified input space. We demonstrate the effectiveness of our procedure on a broad range of benchmarks where, in some instances, we witness a 96% reduction in the number of subproblems during branch-and-bound, and also achieve state-of-the-art verified accuracy across multiple benchmarks. Clip-and-Verify is part of the $α,β$-CROWN verifier (http://abcrown.org), the VNN-COMP 2025 winner. Code available at https://github.com/Verified-Intelligence/Clip_and_Verify.

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arXiv2025

Distributionally Robust Performative Optimization

In performative stochastic optimization, decisions can influence the distribution of random parameters, rendering the data-generating process itself decision-dependent. In practice, decision-makers rarely have access to the true distribution map and must instead rely on imperfect surrogate models, which can lead to severely suboptimal solutions under misspecification. Data scarcity or costly collection further exacerbates these challenges in real-world settings. To address these challenges, we propose a distributionally robust framework for performative optimization that explicitly accounts for ambiguity in the decision-dependent distribution. Our framework introduces three modeling paradigms that capture a broad range of applications in machine learning and decision-making under uncertainty. This latter setting has not previously been explored in the performative optimization literature. To tackle the intractability of the resulting nonconvex objectives, we develop an iterative algorithm named repeated robust risk minimization, which alternates between solving a decision-independent distributionally robust optimization problem and updating the ambiguity set based on the previous decision. This decoupling ensures computational tractability at each iteration while enhancing robustness to model uncertainty. We provide reformulations compatible with off-the-shelf solvers and establish theoretical guarantees on convergence and suboptimality. Extensive numerical experiments in strategic classification, revenue management, and portfolio optimization demonstrate significant performance gains over state-of-the-art baselines, highlighting the practical value of our approach.

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arXiv2025

Distributionally Robust Optimization with Decision-Dependent Information Discovery

We study two-stage distributionally robust optimization (DRO) problems with decision-dependent information discovery (DDID) wherein (a portion of) the uncertain parameters are revealed only if an (often costly) investment is made in the first stage. This class of problems finds many important applications in selection problems (e.g., in hiring, project portfolio optimization, or optimal sensor location). Despite the wide applicability of the problem, it has not been previously studied. We propose a framework for modeling and approximately solving DRO problems with DDID. We formulate the problem as a min-max-min-max problem and adopt the popular K-adaptability approximation scheme, which chooses K candidate recourse actions here-and-now and implements the best of those actions after the uncertain parameters that were chosen to be observed are revealed. We then present a decomposition algorithm that solves the K-adaptable formulation exactly. In particular, we devise a cutting plane algorithm that iteratively solves a relaxed version of the problem, evaluates the true objective value of the corresponding solution, generates valid cuts, and imposes them in the relaxed problem. For the evaluation problem, we develop a branch-and-cut algorithm that provably converges to an optimal solution. We showcase the effectiveness of our framework on the R&D project portfolio optimization problem and the best box problem.

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arXiv2025

Learning Fair Policies for Infectious Diseases Mitigation using Path Integral Control

Infectious diseases pose major public health challenges to society, highlighting the importance of designing effective policies to reduce economic loss and mortality. In this paper, we propose a framework for sequential decision-making under uncertainty to design fairness-aware disease mitigation policies that incorporate various measures of unfairness. Specifically, our approach learns equitable vaccination and lockdown strategies based on a stochastic multi-group SIR model. To address the challenges of solving the resulting sequential decision-making problem, we adopt the path integral control algorithm as an efficient solution scheme. Through a case study, we demonstrate that our approach effectively improves fairness compared to conventional methods and provides valuable insights for policymakers.

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arXiv2024

Sample Complexity of Data-driven Multistage Stochastic Programming under Markovian Uncertainty

This work is motivated by the challenges of applying the sample average approximation (SAA) method to multistage stochastic programming with an unknown continuous-state Markov process. While SAA is widely used in static and two-stage stochastic optimization, it becomes computationally intractable in general multistage settings as the time horizon $T$ increases. Indeed, the number of samples required to obtain a reasonably accurate solution grows exponentially$\text{ -- }$a phenomenon known as the curse of dimensionality with respect to the time horizon. To overcome this limitation, we propose a novel data-driven approach, the Markov Recombining Scenario Tree (MRST) method, which constructs an approximate problem using only two independent trajectories of historical data. Our analysis demonstrates that the MRST method achieves polynomial sample complexity in $T$, providing a more efficient alternative to SAA. Numerical experiments on the Linear Quadratic Gaussian problem show that MRST outperforms SAA, addressing the curse of dimensionality.

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arXiv2024

Generalization Bounds for Contextual Stochastic Optimization using Kernel Regression

In this paper, we consider contextual stochastic optimization using Nadaraya-Watson kernel regression, which is one of the most common approaches in nonparametric regression. Recent studies have explored the asymptotic convergence behavior of using Nadaraya-Watson kernel regression in contextual stochastic optimization; however, the performance guarantee under finite samples remains an open question. This paper derives a finite-sample generalization bound of the Nadaraya-Watson estimator with a spherical kernel under a generic loss function. Based on the generalization bound, we further establish a suboptimality bound for the solution of the Nadaraya-Watson approximation problem relative to the optimal solution. Finally, we derive the optimal kernel bandwidth and provide a sample complexity analysis of the Nadaraya-Watson approximation problem.

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arXiv2024

Distributionally Fair Stochastic Optimization using Wasserstein Distance

A traditional stochastic program under a finite population typically seeks to optimize efficiency by maximizing the expected profits or minimizing the expected costs, subject to a set of constraints. However, implementing such optimization-based decisions can have varying impacts on individuals, and when assessed using the individuals' utility functions, these impacts may differ substantially across demographic groups delineated by sensitive attributes, such as gender, race, age, and socioeconomic status. As each group comprises multiple individuals, a common remedy is to enforce group fairness, which necessitates the measurement of disparities in the distributions of utilities across different groups. This paper introduces the concept of Distributionally Fair Stochastic Optimization (DFSO) based on the Wasserstein fairness measure. The DFSO aims to minimize distributional disparities among groups, quantified by the Wasserstein distance, while adhering to an acceptable level of inefficiency. Our analysis reveals that: (i) the Wasserstein fairness measure recovers the demographic parity fairness prevalent in binary classification literature; (ii) this measure can approximate the well-known Kolmogorov-Smirnov fairness measure with considerable accuracy; and (iii) despite DFSO's biconvex nature, the epigraph of the Wasserstein fairness measure is generally Mixed-Integer Convex Programming Representable (MICP-R). Additionally, we introduce two distinct lower bounds for the Wasserstein fairness measure: the Jensen bound, applicable to the general Wasserstein fairness measure, and the Gelbrich bound, specific to the type-2 Wasserstein fairness measure. We establish the exactness of the Gelbrich bound and quantify the theoretical difference between the Wasserstein fairness measure and the Gelbrich bound.

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arXiv2023

Learning Fair Policies for Multi-stage Selection Problems from Observational Data

We consider the problem of learning fair policies for multi-stage selection problems from observational data. This problem arises in several high-stakes domains such as company hiring, loan approval, or bail decisions where outcomes (e.g., career success, loan repayment, recidivism) are only observed for those selected. We propose a multi-stage framework that can be augmented with various fairness constraints, such as demographic parity or equal opportunity. This problem is a highly intractable infinite chance-constrained program involving the unknown joint distribution of covariates and outcomes. Motivated by the potential impact of selection decisions on people's lives and livelihoods, we propose to focus on interpretable linear selection rules. Leveraging tools from causal inference and sample average approximation, we obtain an asymptotically consistent solution to this selection problem by solving a mixed binary conic optimization problem, which can be solved using standard off-the-shelf solvers. We conduct extensive computational experiments on a variety of datasets adapted from the UCI repository on which we show that our proposed approaches can achieve an 11.6% improvement in precision and a 38% reduction in the measure of unfairness compared to the existing selection policy.

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arXiv2023

Second-order bounds for the M/M/$s$ queue with random arrival rate

Consider an M/M/$s$ queue with the additional feature that the arrival rate is a random variable of which only the mean, variance, and range are known. Using semi-infinite linear programming and duality theory for moment problems, we establish for this setting tight bounds for the expected waiting time. These bounds correspond to an arrival rate that takes only two values. The proofs crucially depend on the fact that the expected waiting time, as function of the arrival rate, has a convex derivative. We apply the novel tight bounds to a rational queueing model, where arriving individuals decide to join or balk based on expected utility and only have partial knowledge about the market size.

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arXiv2023

Distributionally Robust Path Integral Control

We consider a continuous-time continuous-space stochastic optimal control problem, where the controller lacks exact knowledge of the underlying diffusion process, relying instead on a finite set of historical disturbance trajectories. In situations where data collection is limited, the controller synthesized from empirical data may exhibit poor performance. To address this issue, we introduce a novel approach named Distributionally Robust Path Integral (DRPI). The proposed method employs distributionally robust optimization (DRO) to robustify the resulting policy against the unknown diffusion process. Notably, the DRPI scheme shows similarities with risk-sensitive control, which enables us to utilize the path integral control (PIC) framework as an efficient solution scheme. We derive theoretical performance guarantees for the DRPI scheme, which closely aligns with selecting a risk parameter in risk-sensitive control. We validate the efficacy of our scheme and showcase its superiority when compared to risk-neutral PIC policies in the absence of the true diffusion process.

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arXiv2022

Distributionally Robust Chance-Constrained Optimal Transmission Switching for Renewable Integration

Increasing integration of renewable generation poses significant challenges to ensure robustness guarantees in real-time energy system decision-making. This work aims to develop a robust optimal transmission switching (OTS) framework that can effectively relieve grid congestion and mitigate renewable curtailment. We formulate a two-stage distributionally robust chance-constrained (DRCC) problem that assures limited constraint violations for any uncertainty distribution within an ambiguity set. Here, the second-stage recourse variables are represented as linear functions of uncertainty, yielding an equivalent reformulation involving linear constraints only. We utilize moment-based (mean-mean absolute deviation) and distance-based (infinity-Wasserstein distance) ambiguity sets that lead to scalable mixed-integer linear program (MILP) formulations. Numerical experiments on the IEEE 14-bus and 118-bus systems have demonstrated the performance improvements of the proposed DRCC-OTS approaches in terms of guaranteed constraint violations and reduced renewable curtailment. In particular, the computational efficiency of the moment-based MILP approach, which is scenario-free with fixed problem dimensions, has been confirmed, making it suitable for real-time grid operations.

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arXiv2022

Distributionally Robust Observable Strategic Queues

This paper presents an extension of Naor's analysis on the join-or-balk problem in observable M/M/1 queues. While all other Markovian assumptions still hold, we explore this problem assuming uncertain arrival rates under the distributionally robust settings. We first study the problem with the classical moment ambiguity set, where the support, mean, and mean-absolute deviation of the underlying distribution are known. Next, we extend the model to the data-driven setting, where decision makers only have access to a finite set of samples. We develop three optimal joining threshold strategies from the perspective of an individual customer, a social optimizer, and a revenue maximizer, such that their respective worst-case expected benefit rates are maximized. Finally, we compare our findings with Naor's original results and the traditional sample average approximation scheme.

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arXiv2021

On Data-Driven Prescriptive Analytics with Side Information: A Regularized Nadaraya-Watson Approach

We consider generic stochastic optimization problems in the presence of side information which enables a more insightful decision. The side information constitutes observable exogenous covariates that alter the conditional probability distribution of the random problem parameters. A decision maker who adapts her decisions according to the observed side information solves an optimization problem where the objective function is specified by the conditional expectation of the random cost. If the joint probability distribution is unknown, then the conditional expectation can be approximated in a data-driven manner using the Nadaraya-Watson (NW) kernel regression. While the emerging approximation scheme has found successful applications in diverse decision problems under uncertainty, it is largely unknown whether the scheme can provide any reasonable out-of-sample performance guarantees. In this paper, we establish guarantees for the generic problems by leveraging techniques from moderate deviations theory. Our analysis motivates the use of a variance-based regularization scheme which, in general, leads to a non-convex optimization problem. We adopt ideas from distributionally robust optimization to obtain tractable formulations. We present numerical experiments for newsvendor and wind energy commitment problems to highlight the effectiveness of our regularization scheme.

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arXiv2021

A Decision Rule Approach for Two-Stage Data-Driven Distributionally Robust Optimization Problems with Random Recourse

We study two-stage stochastic optimization problems with random recourse, where the adaptive decisions are multiplied with the uncertain parameters in both the objective function and the constraints. To mitigate the computational intractability of infinite-dimensional optimization, we propose a scalable approximation scheme via piecewise linear and piecewise quadratic decision rules. We then develop a data-driven distributionally robust framework with two layers of robustness to address distributionally uncertainty. The emerging optimization problem can be reformulated as an exact copositive program, which admits tractable approximations in semidefinite programming. We design a decomposition algorithm where smaller-size semidefinite programs can be solved in parallel, which further reduces the runtime. Lastly, we establish the performance guarantees of the proposed scheme and demonstrate its effectiveness through numerical examples.

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