arXiv subjects

Prem Talwai

Publications and source records attributed to Prem Talwai.

7 recordsLinked to original sources

arXiv2026

Binomial Smoothing for Inventory and Information Control in Supply Chains

In many decentralized supply chains, upstream firms do not observe market demand directly and instead infer downstream conditions from the order stream. A retailer's replenishment policy therefore plays a dual role: it governs inventory replenishment and shapes the information available for upstream forecasting. This creates a fundamental trade-off. Smoother orders improve upstream predictability, but delaying the response to demand can increase downstream inventory costs. We study how a retailer should optimally smooth demand in a two-tier supply chain with one retailer and one manufacturer when the manufacturer forecasts future orders from the retailer's order history. We propose Binomial Smoothing, a class of replenishment policies that implements delayed demand response by spreading each unit of demand over a finite horizon using binomial weights. The class is interpretable, easy to calibrate, and analytically tractable. Under weakly stationary Gaussian demand satisfying mild regularity conditions, we show that, for any fixed smoothing horizon, the Binomial policy minimizes the manufacturer's forecast error among all policies with the same degree of smoothing. It remains invertible, so the manufacturer can recover demand history from observed orders. More generally, Binomial Smoothing achieves a constant-factor approximation guarantee relative to an optimal policy. Our results yield a broader insight: replenishment policies should be designed not merely to reduce order variance, as in the traditional bullwhip measure, but to reduce the unpredictable component of orders. Carefully designed smoothing can improve supply-chain performance and partially substitute for information sharing, providing a concrete mechanism for coordination without collaboration.

stat.AP↗

arXiv2026

Designing Information Delays in Supply Chains

This paper studies how a downstream retailer in a decentralized two-tier supply chain can implicitly transmit demand information to an upstream supplier through the structure of its order stream in the absence of an explicit information-sharing mechanism. We distinguish our work from prior work by introducing the notion of information delay and by linking optimal implicit information sharing to the group delay of the retailer's ordering transfer function. We show that pure delay is strictly suboptimal, while fractional-delay mechanisms can reshape the order autocorrelation to improve supplier forecastability and reduce system-wide inventory costs. Using Hardy-space factorization, we develop a tractable family of invertible ARMA policies that approximates the theoretically optimal (but non-rational) limiting filter derived by Caldentey et al. (2025) and preserves its informational delay properties. This construction yields sharp guidance on how policy complexity, as measured by the degrees of the ARMA policies, impacts supply chain costs. We further extend the analysis to memory-constrained suppliers and characterize how the complexity of the retailer's policy should scale with the supplier's finite forecasting window, highlighting when, perhaps counterintuitively, increasing policy complexity can become counterproductive.

math.OC↗

arXiv2024

Nonparametric Regression in Dirichlet Spaces: A Random Obstacle Approach

In this paper, we consider nonparametric estimation over general Dirichlet metric measure spaces. Unlike the more commonly studied reproducing kernel Hilbert space, whose elements may be defined pointwise, a Dirichlet space typically only contain equivalence classes, i.e. its elements are only unique almost everywhere. This lack of pointwise definition presents significant challenges in the context of nonparametric estimation, for example the classical ridge regression problem is ill-posed. In this paper, we develop a new technique for renormalizing the ridge loss by replacing pointwise evaluations with certain \textit{local means} around the boundaries of obstacles centered at each data point. The resulting renormalized empirical risk functional is well-posed and even admits a representer theorem in terms of certain equilibrium potentials, which are truncated versions of the associated Green function, cut-off at a data-driven threshold. We demonstrate that the renormalized ridge estimator is rate-optimal, and derive an adaptive upper bound on its convergence rate that highlights the interplay between the analytic, geometric, and probabilistic properties of the Dirichlet form. Our framework notably does not require the smoothness of the underlying space, and is applicable to both manifold and fractal settings. To the best of our knowledge, this is the first paper to obtain optimal, out-of-sample convergence guarantees in the framework of general metric measure Dirichlet spaces.

math.ST↗

arXiv2022

Optimal Learning Rates for Regularized Least-Squares with a Fourier Capacity Condition

We derive minimax adaptive rates for a new, broad class of Tikhonov-regularized learning problems in Hilbert scales under general source conditions. Our analysis does not require the regression function to be contained in the hypothesis class, and most notably does not employ the conventional \textit{a priori} assumptions on kernel eigendecay. Using the theory of interpolation, we demonstrate that the spectrum of the Mercer operator can be inferred in the presence of ``tight'' $L^{\infty}(\mathcal{X})$ embeddings of suitable Hilbert scales. Our analysis utilizes a new Fourier isocapacitary condition, which captures the interplay of the kernel Dirichlet capacities and small ball probabilities via the optimal Hilbert scale function.

math.ST↗

arXiv2021

Dynamic Pricing and Demand Learning on a Large Network of Products: A PAC-Bayesian Approach

We consider a seller offering a large network of $N$ products over a time horizon of $T$ periods. The seller does not know the parameters of the products' linear demand model, and can dynamically adjust product prices to learn the demand model based on sales observations. The seller aims to minimize its pseudo-regret, i.e., the expected revenue loss relative to a clairvoyant who knows the underlying demand model. We consider a sparse set of demand relationships between products to characterize various connectivity properties of the product network. In particular, we study three different sparsity frameworks: (1) $L_0$ sparsity, which constrains the number of connections in the network, and (2) off-diagonal sparsity, which constrains the magnitude of cross-product price sensitivities, and (3) a new notion of spectral sparsity, which constrains the asymptotic decay of a similarity metric on network nodes. We propose a dynamic pricing-and-learning policy that combines the optimism-in-the-face-of-uncertainty and PAC-Bayesian approaches, and show that this policy achieves asymptotically optimal performance in terms of $N$ and $T$. We also show that in the case of spectral and off-diagonal sparsity, the seller can have a pseudo-regret linear in $N$, even when the network is dense.

stat.ML↗

arXiv2021

Sobolev Norm Learning Rates for Conditional Mean Embeddings

We develop novel learning rates for conditional mean embeddings by applying the theory of interpolation for reproducing kernel Hilbert spaces (RKHS). We derive explicit, adaptive convergence rates for the sample estimator under the misspecifed setting, where the target operator is not Hilbert-Schmidt or bounded with respect to the input/output RKHSs. We demonstrate that in certain parameter regimes, we can achieve uniform convergence rates in the output RKHS. We hope our analyses will allow the much broader application of conditional mean embeddings to more complex ML/RL settings involving infinite dimensional RKHSs and continuous state spaces.

stat.ML↗

arXiv2019

A Trace Theorem For Sobolev Spaces On The Sierpinski Gasket

We give a discrete characterization of the trace of a class of Sobolev spaces on the Sierpinski gasket to the bottom line. This includes the L2 domain of the Laplacian as a special case. In addition, for Sobolev spaces of low orders, including the domain of the Dirichlet form, the trace spaces are Besov spaces on the line.

math.CA↗