arXiv subjects

Paat Rusmevichientong

Publications and source records attributed to Paat Rusmevichientong.

8 recordsLinked to original sources

arXiv2026

Inter-Temporal Price Constraints in Dynamic Pricing: Performance Guarantees Under Price Monotonicity and Promotion Fatigue

We study dynamic pricing problems under inter-temporal price constraints. We have resources with limited capacities. At each time period, we decide which products to make available and what prices to charge for the available products. The sale probability for a product depends on its price. If we make a sale for a product, then we collect a revenue reflecting the price and consume the capacities of a combination of resources. We work with two types of inter-temporal constraints. In price monotonicity, the prices charged for a product at different time periods have to be monotone. In promotion fatigue, we can discount a product at most once over each time interval of a fixed length. Computing the optimal policy is intractable. We use fluid approximations to construct policies. Traditionally, policies from fluid approximations make randomized decisions at each time period by following an optimal solution to the fluid approximation, but such randomized decisions easily violate price monotonicity or promotion fatigue constraints. We develop policies that sample price paths according to an optimal solution to the fluid approximation, while satisfying the inter-temporal constraints. Letting $c_{\min}$ be the smallest initial capacity of a resource and $L$ be the maximum number of resources used by a product, our policies have a performance guarantee of $\max\Big\{ \frac{1}{8L}, \, \frac{1}{2} - \sqrt{\frac{\log c_{\min}}{2 \,c_{\min}}} - \frac{L}{c_{\min}}\Big\}$. Thus, under large resource capacities, our policies are guaranteed to obtain at least half of the optimal total expected revenue. The latter performance guarantee is tight in the sense that no policy can, in general, obtain more than half of the optimal objective value of the fluid approximation even under large resource capacities. We unify our approach to open the path for extensions to other inter-temporal price constraints.

math.OC↗

arXiv2024

Revenue Management with Calendar-Aware and Dependent Demands: Asymptotically Tight Fluid Approximations

When modeling the demand in revenue management systems, a natural approach is to focus on a canonical interval of time, such as a week, so that we forecast the demand over each week in the selling horizon. Ideally, we would like to use random variables with general distributions to model the demand over each week. The current demand can give a signal for the future demand, so we also would like to capture the dependence between the demands over different weeks. Prevalent demand models in the literature, which are based on a discrete-time approximation to a Poisson process, are not compatible with these needs. In this paper, we focus on revenue management models that are compatible with a natural approach for forecasting the demand. Building such models through dynamic programming is not difficult. We divide the selling horizon into multiple stages, each stage being a canonical interval of time on the calendar. We have random number of customer arrivals in each stage, whose distribution is arbitrary and depends on the number of arrivals in the previous stage. The question we seek to answer is the form of the corresponding fluid approximation. We give the correct fluid approximation in the sense that it yields asymptotically optimal policies. The form of our fluid approximation is surprising as its constraints use expected capacity consumption of a resource up to a certain time period, conditional on the demand in the stage just before the time period in question. As the resource capacities and number of stages increase with the same rate, our performance guarantee converges to one. To our knowledge, this result gives the first asymptotically optimal policy under dependent demands with arbitrary distributions. Our computational experiments indicate that using the correct fluid approximation can make a dramatic impact in practice.

math.OC↗

arXiv2022

Debiasing In-Sample Policy Performance for Small-Data, Large-Scale Optimization

Motivated by the poor performance of cross-validation in settings where data are scarce, we propose a novel estimator of the out-of-sample performance of a policy in data-driven optimization.Our approach exploits the optimization problem's sensitivity analysis to estimate the gradient of the optimal objective value with respect to the amount of noise in the data and uses the estimated gradient to debias the policy's in-sample performance. Unlike cross-validation techniques, our approach avoids sacrificing data for a test set, utilizes all data when training and, hence, is well-suited to settings where data are scarce. We prove bounds on the bias and variance of our estimator for optimization problems with uncertain linear objectives but known, potentially non-convex, feasible regions. For more specialized optimization problems where the feasible region is "weakly-coupled" in a certain sense, we prove stronger results. Specifically, we provide explicit high-probability bounds on the error of our estimator that hold uniformly over a policy class and depends on the problem's dimension and policy class's complexity. Our bounds show that under mild conditions, the error of our estimator vanishes as the dimension of the optimization problem grows, even if the amount of available data remains small and constant. Said differently, we prove our estimator performs well in the small-data, large-scale regime. Finally, we numerically compare our proposed method to state-of-the-art approaches through a case-study on dispatching emergency medical response services using real data. Our method provides more accurate estimates of out-of-sample performance and learns better-performing policies.

math.OC↗

arXiv2020

Future Evolution of COVID-19 Pandemic in North Carolina: Can We Flatten the Curve?

On June 24th, Governor Cooper announced that North Carolina will not be moving into Phase 3 of its reopening process at least until July 17th. Given the recent increases in daily positive cases and hospitalizations, this decision was not surprising. However, given the political and economic pressures which are forcing the state to reopen, it is not clear what actions will help North Carolina to avoid the worst. We use a compartmentalized model to study the effects of social distancing measures and testing capacity combined with contact tracing on the evolution of the pandemic in North Carolina until the end of the year. We find that going back to restrictions that were in place during Phase 1 will slow down the spread but if the state wants to continue to reopen or at least remain in Phase 2 or Phase 3 it needs to significantly expand its testing and contact tracing capacity. Even under our best-case scenario of high contact tracing effectiveness, the number of contact tracers the state currently employs is inadequate.

q-bio.PE↗

arXiv2020

Can Testing Ease Social Distancing Measures? Future Evolution of COVID-19 in NYC

The "New York State on Pause" executive order came into effect on March 22 with the goal of ensuring adequate social distancing to alleviate the spread of COVID-19. Pause will remain effective in New York City in some form until early June. We use a compartmentalized model to study the effects of testing capacity and social distancing measures on the evolution of the pandemic in the "post-Pause" period in the City. We find that testing capacity must increase dramatically if it is to counterbalance even relatively small relaxations in social distancing measures in the immediate post-Pause period. In particular, if the City performs 20,000 tests per day and relaxes the social distancing measures to the pre-Pause norms, then the total number of deaths by the end of September can reach 250,000. By keeping the social distancing measures to somewhere halfway between the pre- and in-Pause norms and performing 100,000 tests per day, the total number of deaths by the end of September can be kept at around 27,000. Going back to the pre-Pause social distancing norms quickly must be accompanied by an exorbitant testing capacity, if one is to suppress excessive deaths. If the City is to go back to the "pre-Pause" social distancing norms in the immediate post-Pause period and keep the total number of deaths by the end of September at around 35,000, then it should be performing 500,000 tests per day. Our findings have important implications on the magnitude of the testing capacity the City needs as it relaxes the social distancing measures to reopen its economy.

q-bio.PE↗

arXiv2016

Efficient Empirical Bayes prediction under check loss using Asymptotic Risk Estimates

We develop a novel Empirical Bayes methodology for prediction under check loss in high-dimensional Gaussian models. The check loss is a piecewise linear loss function having differential weights for measuring the amount of underestimation or overestimation. Prediction under it differs in fundamental aspects from estimation or prediction under weighted-quadratic losses. Because of the nature of this loss, our inferential target is a pre-chosen quantile of the predictive distribution rather than the mean of the predictive distribution. We develop a new method for constructing uniformly efficient asymptotic risk estimates which are then minimized to produce effective linear shrinkage predictive rules. In calculating the magnitude and direction of shrinkage, our proposed predictive rules incorporate the asymmetric nature of the loss function and are shown to be asymptotically optimal. Using numerical experiments we compare the performance of our method with traditional Empirical Bayes procedures and obtain encouraging results.

math.ST↗

arXiv2013

A Tractable POMDP for a Class of Sequencing Problems

We consider a partially observable Markov decision problem (POMDP) that models a class of sequencing problems. Although POMDPs are typically intractable, our formulation admits tractable solution. Instead of maintaining a value function over a high-dimensional set of belief states, we reduce the state space to one of smaller dimension, in which grid-based dynamic programming techniques are effective. We develop an error bound for the resulting approximation, and discuss an application of the model to a problem in targeted advertising.

cs.AI↗

arXiv2010

Linearly Parameterized Bandits

We consider bandit problems involving a large (possibly infinite) collection of arms, in which the expected reward of each arm is a linear function of an $r$-dimensional random vector $\mathbf{Z} \in \mathbb{R}^r$, where $r \geq 2$. The objective is to minimize the cumulative regret and Bayes risk. When the set of arms corresponds to the unit sphere, we prove that the regret and Bayes risk is of order $Θ(r \sqrt{T})$, by establishing a lower bound for an arbitrary policy, and showing that a matching upper bound is obtained through a policy that alternates between exploration and exploitation phases. The phase-based policy is also shown to be effective if the set of arms satisfies a strong convexity condition. For the case of a general set of arms, we describe a near-optimal policy whose regret and Bayes risk admit upper bounds of the form $O(r \sqrt{T} \log^{3/2} T)$.

cs.LG↗