arXiv subjects

Napat Rujeerapaiboon

Publications and source records attributed to Napat Rujeerapaiboon.

7 recordsLinked to original sources

arXiv2026

Equitable Auction Design with Provable Regret Guarantees

We study a mechanism design problem where a seller aims to allocate a good to multiple bidders, each with a private value. The seller supports or favors a specific group, referred to as the minority group. Specifically, the seller requires that allocations to the minority group are at least a predetermined fraction (equity level) of those made to the rest of the bidders. We include the equity requirements as constraints in the design of a mechanism, and our goal is to characterize equitable mechanisms with provable performance guarantees. Motivated by settings where reliable information about the bidders' values is unavailable, our main focus is a regret-based mechanism design problem, which makes no assumptions about the distribution of the bidders' values and aims to minimize the maximum ex-post regret. Here, regret is defined as the difference between the highest revenue achievable in hindsight and the revenue generated by a mechanism. We propose a closed-form mechanism and prove that its ex-post regret is at most a constant multiple (dependent on the equity level) of the optimal worst-case regret. When bidders' value supports are identical, this factor is less than 1.31 across all equity levels. As a benchmark, we also study a stochastic mechanism design problem that assumes known bidder value distributions and maximizes expected revenue. We characterize the optimal mechanism under standard independence and regularity assumptions. Both mechanisms can be interpreted as set-asides, a common policy tool that reserves a fraction of goods for minority groups. Numerical results demonstrate that the stochastic mechanism performs well when the bidders' value distribution is accurately estimated, while the regret-based mechanism exhibits greater robustness under estimation errors.

econ.TH↗

arXiv2025

Robust Conic Satisficing

In practical optimization problems, we typically model uncertainty as a random variable though its true probability distribution is unobservable to the decision maker. Historical data provides some information of this distribution that we can use to approximately quantify the risk that depends on both the decision and the uncertainty. This empirical optimization approach is vulnerable to the issues of overfitting, which could be overcome by several data-driven robust optimization techniques. To tackle overfitting, Long et.al.(2022) propose a robust satisficing model, which is specified by a performance target and a penalty function that measures the deviation of the uncertainty from its nominal value, and yields solutions with superior out-of-sample performance. We generalize the robust satisficing framework to conic optimization problems with recourse, which has broad applications in predictive and prescriptive analytics. We derive an exact semidefinite optimization formulation for a biconvex quadratic evaluation function, with quadratic penalty and ellipsoidal support set. More importantly, under complete and bounded recourse, and a reasonably chosen polyhedral support set and penalty function, we propose safe approximations that are feasible for any reasonably chosen target. We then demonstrate that the assumption of complete and bounded recourse is not unimpeachable, and then introduce a novel perspective casting technique to derive an equivalent conic optimization problem satisfying the stated assumptions. Computationally, we showcase a study on data-driven portfolio optimization and demonstrate that the robust satisficing solutions can provide significant improvements over the solutions obtained by stochastic optimization models, including the celebrated Markowitz model, which is prone to overfitting.

math.OC↗

arXiv2022

A Planner-Trader Decomposition for Multi-Market Hydro Scheduling

Peak/off-peak spreads on European electricity forward and spot markets are eroding due to the ongoing nuclear phaseout in Germany and the steady growth in photovoltaic capacity. The reduced profitability of peak/off-peak arbitrage forces hydropower producers to recover part of their original profitability on the reserve markets. We propose a bi-layer stochastic programming framework for the optimal operation of a fleet of interconnected hydropower plants that sells energy on both the spot and the reserve markets. The outer layer (the planner's problem) optimizes end-of-day reservoir filling levels over one year, whereas the inner layer (the trader's problem) selects optimal hourly market bids within each day. Using an information restriction whereby the planner prescribes the end-of-day reservoir targets one day in advance, we prove that the trader's problem simplifies from an infinite-dimensional stochastic program with 25 stages to a finite two-stage stochastic program with only two scenarios. Substituting this reformulation back into the outer layer and approximating the reservoir targets by affine decision rules allows us to simplify the planner's problem from an infinite-dimensional stochastic program with 365 stages to a two-stage stochastic program that can conveniently be solved via the sample average approximation. Numerical experiments based on a cascade in the Salzburg region of Austria demonstrate the effectiveness of the suggested framework.

math.OC↗

arXiv2019

Size Matters: Cardinality-Constrained Clustering and Outlier Detection via Conic Optimization

Plain vanilla K-means clustering has proven to be successful in practice, yet it suffers from outlier sensitivity and may produce highly unbalanced clusters. To mitigate both shortcomings, we formulate a joint outlier detection and clustering problem, which assigns a prescribed number of datapoints to an auxiliary outlier cluster and performs cardinality-constrained K-means clustering on the residual dataset, treating the cluster cardinalities as a given input. We cast this problem as a mixed-integer linear program (MILP) that admits tractable semidefinite and linear programming relaxations. We propose deterministic rounding schemes that transform the relaxed solutions to feasible solutions for the MILP. We also prove that these solutions are optimal in the MILP if a cluster separation condition holds.

math.OC↗

arXiv2017

Scenario Reduction Revisited: Fundamental Limits and Guarantees

The goal of scenario reduction is to approximate a given discrete distribution with another discrete distribution that has fewer atoms. We distinguish continuous scenario reduction, where the new atoms may be chosen freely, and discrete scenario reduction, where the new atoms must be chosen from among the existing ones. Using the Wasserstein distance as measure of proximity between distributions, we identify those $n$-point distributions on the unit ball that are least susceptible to scenario reduction, i.e., that have maximum Wasserstein distance to their closest $m$-point distributions for some prescribed $m<n$. We also provide sharp bounds on the added benefit of continuous over discrete scenario reduction. Finally, to our best knowledge, we propose the first polynomial-time constant-factor approximations for both discrete and continuous scenario reduction as well as the first exact exponential-time algorithms for continuous scenario reduction.

math.OC↗

arXiv2016

Multi-Period Portfolio Optimization: Translation of Autocorrelation Risk to Excess Variance

Growth-optimal portfolios are guaranteed to accumulate higher wealth than any other investment strategy in the long run. However, they tend to be risky in the short term. For serially uncorrelated markets, similar portfolios with more robust guarantees have been recently proposed. This paper extends these robust portfolios by accommodating non-zero autocorrelations that may reflect investors' beliefs about market movements. Moreover, we prove that the risk incurred by such autocorrelations can be absorbed by modifying the covariance matrix of asset returns.

q-fin.PM↗

arXiv2016

Chebyshev Inequalities for Products of Random Variables

We derive sharp probability bounds on the tails of a product of symmetric non-negative random variables using only information about their first two moments. If the covariance matrix of the random variables is known exactly, these bounds can be computed numerically using semidefinite programming. If only an upper bound on the covariance matrix is available, the probability bounds on the right tails can be evaluated analytically. The bounds under precise and imprecise covariance information coincide for all left tails as well as for all right tails corresponding to quantiles that are either sufficiently small or sufficiently large. We also prove that all left probability bounds reduce to the trivial bound 1 if the number of random variables in the product exceeds an explicit threshold. Thus, in the worst case, the weak-sense geometric random walk defined through the running product of the random variables is absorbed at 0 with certainty as soon as time exceeds the given threshold. The techniques devised for constructing Chebyshev bounds for products can also be used to derive Chebyshev bounds for sums, maxima and minima of non-negative random variables.

math.PR↗