arXiv subjects

Ali Eshragh

Publications and source records attributed to Ali Eshragh.

At least 19 recordsLinked to original sources

arXiv2026

Modified Dynamic Programming Algorithms for Order Picking in Single-Block and Two-Block Rectangular Warehouses

Recent research has shown that optimal picker tours in rectangular warehouses exhibit deterministic travel patterns within each aisle, and that certain previously considered traversals are unnecessary. Using these insights, this paper proposes modifications to dynamic programming algorithms that improve computational efficiency without affecting optimality. For layouts with and without a central cross-aisle, the modifications preserve linear-time complexity in the number of aisles while reducing the number of state-action evaluations per stage. The proposed modifications reduce computational effort by factors up to 1.81, confirmed by numerical experiments. These findings are encouraging and highlight how structural refinements can yield significant improvements in practical performance of algorithms.

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arXiv2025

Double Traversals in Boundary Subaisles: Implications for Two-Block Layouts

The order picking problem seeks the shortest warehouse route that visits all required item locations. Strict conditions are known for single-block rectangular layouts under which optimal routes never require double traversals, while broader results show that double traversals serving cross-aisle connectivity can always be avoided. We strengthen these findings by proving that no double traversals are needed in the boundary subaisles, the uppermost and lowermost subaisle segments, of warehouses with at least two non-empty aisles. This yields a unified strict condition for all single-block layouts and for two-block layouts with more than one aisle. For these widely used layouts, exact methods such as dynamic programming and mathematical programming can therefore exclude the double-traversal configuration from every boundary subaisle, reducing the number of admissible edge configurations without loss of optimality.

math.OC↗

arXiv2025

Reflections from Research Roundtables at the Conference on Health, Inference, and Learning (CHIL) 2025

The 6th Annual Conference on Health, Inference, and Learning (CHIL 2025), hosted by the Association for Health Learning and Inference (AHLI), was held in person on June 25-27, 2025, at the University of California, Berkeley, in Berkeley, California, USA. As part of this year's program, we hosted Research Roundtables to catalyze collaborative, small-group dialogue around critical, timely topics at the intersection of machine learning and healthcare. Each roundtable was moderated by a team of senior and junior chairs who fostered open exchange, intellectual curiosity, and inclusive engagement. The sessions emphasized rigorous discussion of key challenges, exploration of emerging opportunities, and collective ideation toward actionable directions in the field. In total, eight roundtables were held by 19 roundtable chairs on topics of "Explainability, Interpretability, and Transparency," "Uncertainty, Bias, and Fairness," "Causality," "Domain Adaptation," "Foundation Models," "Learning from Small Medical Data," "Multimodal Methods," and "Scalable, Translational Healthcare Solutions."

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arXiv2025

Deterministic Structure of Vertical Configurations in Minimal Picker Tours for Rectangular Warehouses

The picker routing problem seeks the shortest tour through a warehouse that visits every item in a given pick-list and returns to the depot. For rectangular warehouses, dynamic programming algorithms solve this problem by sequentially evaluating combinations of vertical edge configurations within subaisles and horizontal edge configurations between aisles. These methods proceed through stages one after another, but how those stages relate to each other has received limited structural analysis. Building on our recent structural result for rectangular warehouses, which shows that connecting double traversals are not required to maintain tour connectivity, we prove that for rectangular warehouses of any size, the horizontal edge structure of a minimal tour subgraph uniquely determines the required vertical edge configurations. The proof uses a case analysis on horizontal degree along each aisle and at merged-segment endpoints, showing that the admissible vertical pattern in each regime is uniquely determined by Eulerian parity and by minimizing traversal length. This deterministic relationship implies that vertical configuration stages in existing dynamic programming algorithms can be replaced by a direct inference step, reducing the combinatorial complexity of the problem and providing a structural foundation for developing more efficient exact methods for warehouse layouts of any size.

math.OC↗

arXiv2025

Ranking Vectors Clustering: Theory and Applications

We study the problem of clustering ranking vectors, where each vector represents preferences as an ordered list of distinct integers. Specifically, we focus on the k-centroids ranking vectors clustering problem (KRC), which aims to partition a set of ranking vectors into k clusters and identify the centroid of each cluster. Unlike classical k-means clustering (KMC), KRC constrains both the observations and centroids to be ranking vectors. We establish the NP-hardness of KRC and characterize its feasible set. For the single-cluster case, we derive a closed-form analytical solution for the optimal centroid, which can be computed in linear time. To address the computational challenges of KRC, we develop an efficient approximation algorithm, KRCA, which iteratively refines initial solutions from KMC, referred to as the baseline solution. Additionally, we introduce a branch-and-bound (BnB) algorithm for efficient cluster reconstruction within KRCA, leveraging a decision tree framework to reduce computational time while incorporating a controlling parameter to balance solution quality and efficiency. We establish theoretical error bounds for KRCA and BnB. Through extensive numerical experiments on synthetic and real-world datasets, we demonstrate that KRCA consistently outperforms baseline solutions, delivering significant improvements in solution quality with fast computational times. This work highlights the practical significance of KRC for personalization and large-scale decision making, offering methodological advancements and insights that can be built upon in future studies.

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arXiv2025

Double Traversals in Optimal Picker Routes for Warehouses with Multiple Blocks

Order picking is a process that involves collecting items from their respective locations within a warehouse. There exist dynamic programming algorithms for finding the minimal picker route by considering only a limited number of options for possible travel within a subaisle. Although one such action, traversing an aisle twice, has been shown to never be required for a rectangular warehouse with two cross-aisles, this is not the case when there are more than two cross-aisles. In this work, we demonstrate that double traversals within a subaisle are not required to connect cross-aisle travel regardless of the number of cross-aisles. This result simplifies the structure of feasible tours, enabling more efficient algorithms.

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arXiv2024

Efficient Data-Driven Leverage Score Sampling Algorithm for the Minimum Volume Covering Ellipsoid Problem in Big Data

The Minimum Volume Covering Ellipsoid (MVCE) problem, characterised by $n$ observations in $d$ dimensions where $n \gg d$, can be computationally very expensive in the big data regime. We apply methods from randomised numerical linear algebra to develop a data-driven leverage score sampling algorithm for solving MVCE, and establish theoretical error bounds and a convergence guarantee. Assuming the leverage scores follow a power law decay, we show that the computational complexity of computing the approximation for MVCE is reduced from $\mathcal{O}(nd^2)$ to $\mathcal{O}(nd + \text{poly}(d))$, which is a significant improvement in big data problems. Numerical experiments demonstrate the efficacy of our new algorithm, showing that it substantially reduces computation time and yields near-optimal solutions.

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arXiv2024

A Modified Algorithm for Optimal Picker Routing in a Single Block Warehouse

The order picker routing problem involves finding the optimal tour of a warehouse that collects all the required items on a given pick list. Ratliff and Rosenthal introduced a dynamic programming algorithm for solving this problem in polynomial time by sequentially adding edges inside and between each aisle to construct a tour. We provide a method where only transitions from one aisle to the next are considered, significantly reducing the number of stages in the algorithm.

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arXiv2024

Deep Reinforcement Learning for Dynamic Order Picking in Warehouse Operations

Order picking is a pivotal operation in warehouses that directly impacts overall efficiency and profitability. This study addresses the dynamic order picking problem, a significant concern in modern warehouse management, where real-time adaptation to fluctuating order arrivals and efficient picker routing are crucial. Traditional methods, which often depend on static optimization algorithms designed around fixed order sets for the picker routing, fall short in addressing the challenges of this dynamic environment. To overcome these challenges, we propose a Deep Reinforcement Learning (DRL) framework tailored for single-block warehouses equipped with an autonomous picking device. By dynamically optimizing picker routes, our approach significantly reduces order throughput times and unfulfilled orders, particularly under high order arrival rates. We benchmark our DRL model against established algorithms, utilizing instances generated based on standard practices in the order picking literature. Experimental results demonstrate the superiority of our DRL model over benchmark algorithms. For example, at a high order arrival rate of 0.09 (i.e., 9 orders per 100 units of time on average), our approach achieves an order fulfillment rate of approximately 98%, compared to the 82% fulfillment rate observed with benchmarking algorithms. We further investigate the integration of a hyperparameter in the reward function that allows for flexible balancing between distance traveled and order completion time. Finally, we demonstrate the robustness of our DRL model on out-of-sample test instances.

math.OC↗

arXiv2024

Optimal Experimental Design for Partially Observable Pure Birth Processes

We develop an efficient algorithm to find optimal observation times by maximizing the Fisher information for the birth rate of a partially observable pure birth process involving $n$ observations. Partially observable implies that at each of the $n$ observation time points for counting the number of individuals present in the pure birth process, each individual is observed independently with a fixed probability $p$, modeling detection difficulties or constraints on resources. We apply concepts and techniques from generating functions, using a combination of symbolic and numeric computation, to establish a recursion for evaluating and optimizing the Fisher information. Our numerical results reveal the efficacy of this new method. An implementation of the algorithm is available publicly.

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arXiv2024

Deep Reinforcement Learning for Picker Routing Problem in Warehousing

Order Picker Routing is a critical issue in Warehouse Operations Management. Due to the complexity of the problem and the need for quick solutions, suboptimal algorithms are frequently employed in practice. However, Reinforcement Learning offers an appealing alternative to traditional heuristics, potentially outperforming existing methods in terms of speed and accuracy. We introduce an attention based neural network for modeling picker tours, which is trained using Reinforcement Learning. Our method is evaluated against existing heuristics across a range of problem parameters to demonstrate its efficacy. A key advantage of our proposed method is its ability to offer an option to reduce the perceived complexity of routes.

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arXiv2023

SALSA: Sequential Approximate Leverage-Score Algorithm with Application in Analyzing Big Time Series Data

We develop a new efficient sequential approximate leverage score algorithm, SALSA, using methods from randomized numerical linear algebra (RandNLA) for large matrices. We demonstrate that, with high probability, the accuracy of SALSA's approximations is within $(1 + O({\varepsilon}))$ of the true leverage scores. In addition, we show that the theoretical computational complexity and numerical accuracy of SALSA surpass existing approximations. These theoretical results are subsequently utilized to develop an efficient algorithm, named LSARMA, for fitting an appropriate ARMA model to large-scale time series data. Our proposed algorithm is, with high probability, guaranteed to find the maximum likelihood estimates of the parameters for the true underlying ARMA model. Furthermore, it has a worst-case running time that significantly improves those of the state-of-the-art alternatives in big data regimes. Empirical results on large-scale data strongly support these theoretical results and underscore the efficacy of our new approach.

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arXiv2022

Large Markov Decision Processes and Combinatorial Optimization

Markov decision processes continue to gain in popularity for modeling a wide range of applications ranging from analysis of supply chains and queuing networks to cognitive science and control of autonomous vehicles. Nonetheless, they tend to become numerically intractable as the size of the model grows fast. Recent works use machine learning techniques to overcome this crucial issue, but with no convergence guarantee. This note provides a brief overview of literature on solving large Markov decision processes, and exploiting them to solve important combinatorial optimization problems.

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arXiv2022

A Hybrid Statistical-Machine Learning Approach for Analysing Online Customer Behavior: An Empirical Study

We apply classical statistical methods in conjunction with the state-of-the-art machine learning techniques to develop a hybrid interpretable model to analyse 454,897 online customers' behavior for a particular product category at the largest online retailer in China, that is JD. While most mere machine learning methods are plagued by the lack of interpretability in practice, our novel hybrid approach will address this practical issue by generating explainable output. This analysis involves identifying what features and characteristics have the most significant impact on customers' purchase behavior, thereby enabling us to predict future sales with a high level of accuracy, and identify the most impactful variables. Our results reveal that customers' product choice is insensitive to the promised delivery time, but this factor significantly impacts customers' order quantity. We also show that the effectiveness of various discounting methods depends on the specific product and the discount size. We identify product classes for which certain discounting approaches are more effective and provide recommendations on better use of different discounting tools. Customers' choice behavior across different product classes is mostly driven by price, and to a lesser extent, by customer demographics. The former finding asks for exercising care in deciding when and how much discount should be offered, whereas the latter identifies opportunities for personalized ads and targeted marketing. Further, to curb customers' batch ordering behavior and avoid the undesirable Bullwhip effect, JD should improve its logistics to ensure faster delivery of orders.

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arXiv2021

Toeplitz Least Squares Problems, Fast Algorithms and Big Data

In time series analysis, when fitting an autoregressive model, one must solve a Toeplitz ordinary least squares problem numerous times to find an appropriate model, which can severely affect computational times with large data sets. Two recent algorithms (LSAR and Repeated Halving) have applied randomized numerical linear algebra (RandNLA) techniques to fitting an autoregressive model to big time-series data. We investigate and compare the quality of these two approximation algorithms on large-scale synthetic and real-world data. While both algorithms display comparable results for synthetic datasets, the LSAR algorithm appears to be more robust when applied to real-world time series data. We conclude that RandNLA is effective in the context of big-data time series.

stat.ML↗

arXiv2021

Rollage: Efficient Rolling Average Algorithm to Estimate ARMA Models for Big Time Series Data

We develop a new efficient algorithm for the analysis of large-scale time series data. We firstly define rolling averages, derive their analytical properties, and establish their asymptotic distribution. These theoretical results are subsequently exploited to develop an efficient algorithm, called Rollage, for fitting an appropriate AR model to big time series data. When used in conjunction with the Durbin's algorithm, we show that the Rollage algorithm can be used as a criterion to optimally fit ARMA models to big time series data. Empirical experiments on large-scale synthetic time series data support the theoretical results and reveal the efficacy of this new approach, especially when compared to existing methodology.

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arXiv2020

Surprise Maximization: A Dynamic Programming Approach

Borwein et al. (2000) solved a surprise maximization problem by applying results from convex analysis and mathematical programming. Although, their proof is elegant, it requires advanced knowledge from both areas to understand it. Here, we provide another approach to derive an optimal solution of the problem by utilizing dynamic programming.

math.OC↗

arXiv2020

Average-reward model-free reinforcement learning: a systematic review and literature mapping

Reinforcement learning is important part of artificial intelligence. In this paper, we review model-free reinforcement learning that utilizes the average reward optimality criterion in the infinite horizon setting. Motivated by the solo survey by Mahadevan (1996a), we provide an updated review of work in this area and extend it to cover policy-iteration and function approximation methods (in addition to the value-iteration and tabular counterparts). We present a comprehensive literature mapping. We also identify and discuss opportunities for future work.

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