arXiv subjects

Seungki Min

Publications and source records attributed to Seungki Min.

9 recordsLinked to original sources

arXiv2025

On the Optimality of Tracking Fisher Information in Adaptive Testing with Stochastic Binary Responses

We study the problem of estimating a continuous ability parameter from sequential binary responses by actively asking questions with varying difficulties, a setting that arises naturally in adaptive testing and online preference learning. Our goal is to certify that the estimate lies within a desired margin of error, using as few queries as possible. We propose a simple algorithm that adaptively selects questions to maximize Fisher information and updates the estimate using a method-of-moments approach, paired with a novel test statistic to decide when the estimate is accurate enough. We prove that this Fisher-tracking strategy achieves optimal performance in both fixed-confidence and fixed-budget regimes, which are commonly invested in the best-arm identification literature. Our analysis overcomes a key technical challenge in the fixed-budget setting -- handling the dependence between the evolving estimate and the query distribution -- by exploiting a structural symmetry in the model and combining large deviation tools with Ville's inequality. Our results provide rigorous theoretical support for simple and efficient adaptive testing procedures.

stat.ML↗

arXiv2025

Dynamic Pricing of an Expiring Item under Strategic Buyers with Stochastic Arrival

We study the optimal dynamic pricing of an expiring ticket or voucher, sold by a time-sensitive seller to strategic buyers who arrive stochastically with private values. The expiring nature creates a conflict: the seller's urgency to sell before expiration drives price reductions, which in turn incentivize buyers to wait. We seek the seller's optimal pricing policy that resolves this tension. The main analytical challenge is that buyer type is two-dimensional (valuation and arrival time), which makes equilibrium intractable under general strategies. To address this, we introduce the Value-Based Threshold (VBT) strategy, a tractable framework that decouples these two dimensions. Using this framework, we prove equilibrium existence via an ordinary differential equation and provide a constructive procedure for its characterization. We then derive near-optimal pricing policies for two stylized regimes: a constant price in thin markets and a linear discount in thick markets. Numerical frontier analysis confirms these benchmarks and shows how optimal policy adapts as the seller's time sensitivity changes. Our findings clarify the conflict between quick sales and strategic waiting. Sellers facing thick markets or high time sensitivity benefit from linear discounts, while in thin markets a constant price neutralizes buyers' incentive to wait. We also show this simple policy remains robust across broad conditions. For patient sellers, a quasi-auction schedule that maintains a high price until a sharp final drop is most effective in aggregating demand.

cs.GT↗

arXiv2024

Improving Thompson Sampling via Information Relaxation for Budgeted Multi-armed Bandits

We consider a Bayesian budgeted multi-armed bandit problem, in which each arm consumes a different amount of resources when selected and there is a budget constraint on the total amount of resources that can be used. Budgeted Thompson Sampling (BTS) offers a very effective heuristic to this problem, but its arm-selection rule does not take into account the remaining budget information. We adopt \textit{Information Relaxation Sampling} framework that generalizes Thompson Sampling for classical $K$-armed bandit problems, and propose a series of algorithms that are randomized like BTS but more carefully optimize their decisions with respect to the budget constraint. In a one-to-one correspondence with these algorithms, a series of performance benchmarks that improve the conventional benchmark are also suggested. Our theoretical analysis and simulation results show that our algorithms (and our benchmarks) make incremental improvements over BTS (respectively, the conventional benchmark) across various settings including a real-world example.

cs.LG↗

arXiv2023

An Information-Theoretic Analysis of Nonstationary Bandit Learning

In nonstationary bandit learning problems, the decision-maker must continually gather information and adapt their action selection as the latent state of the environment evolves. In each time period, some latent optimal action maximizes expected reward under the environment state. We view the optimal action sequence as a stochastic process, and take an information-theoretic approach to analyze attainable performance. We bound limiting per-period regret in terms of the entropy rate of the optimal action process. The bound applies to a wide array of problems studied in the literature and reflects the problem's information structure through its information-ratio.

cs.LG↗

arXiv2023

The Competition for Partners in Matching Markets

We study the competition for partners in two-sided matching markets with heterogeneous agent preferences, with a focus on how the equilibrium outcomes depend on the connectivity in the market. We model random partially connected markets, with each agent having an average degree $d$ in a random (undirected) graph, and a uniformly random preference ranking over their neighbors in the graph. We formally characterize stable matchings in large markets random with small imbalance and find a threshold in the connectivity $d$ at $\log^2 n$ (where $n$ is the number of agents on one side of the market) which separates a ``weak competition'' regime, where agents on both sides of the market do equally well, from a ``strong competition'' regime, where agents on the short (long) side of the market enjoy a significant advantage (disadvantage). Numerical simulations confirm and sharpen our theoretical predictions, and demonstrate robustness to our assumptions. We leverage our characterizations in two ways: First, we derive prescriptive insights into how to design the connectivity of the market to trade off optimally between the average agent welfare achieved and the number of agents who remain unmatched in the market. For most market primitives, we find that the optimal connectivity should lie in the weak competition regime or at the threshold between the regimes. Second, our analysis uncovers a new conceptual principle governing whether the short side enjoys a significant advantage in a given matching market, which can moreover be applied as a diagnostic tool given only basic summary statistics for the market. Counterfactual analyses using data on centralized high school admissions in a major USA city show the practical value of both our design insights and our diagnostic principle.

cs.GT↗

arXiv2022

Risk-Sensitive Optimal Execution via a Conditional Value-at-Risk Objective

We consider a liquidation problem in which a risk-averse trader tries to liquidate a fixed quantity of an asset in the presence of market impact and random price fluctuations. The trader encounters a trade-off between the transaction costs incurred due to market impact and the volatility risk of holding the position. Our formulation begins with a continuous-time and infinite horizon variation of the seminal model of Almgren and Chriss (2000), but we define as the objective the conditional value-at-risk (CVaR) of the implementation shortfall, and allow for dynamic (adaptive) trading strategies. In this setting, we are able to derive closed-form expressions for the optimal liquidation strategy and its value function. Our results yield a number of important practical insights. We are able to quantify the benefit of adaptive policies over optimized static policies. The relevant improvement depends only on the level of risk aversion: for moderate levels of risk aversion, the optimal dynamic policy outperforms the optimal static policy by 5-15%, and outperforms the optimal volume weighted average price (VWAP) policy by 15-25%. This improvement is achieved through dynamic policies that exhibit "aggressiveness-in-the-money": trading is accelerated when price movements are favorable, and is slowed when price movements are unfavorable. From a mathematical perspective, our analysis exploits the dual representation of CVaR to convert the problem to a continuous-time, zero-sum game. We leverage the idea of the state-space augmentation, and obtain a partial differential equation describing the optimal value function, which is separable and a special instance of the Emden-Fowler equation. This leads to a closed-form solution. As our problem is a special case of a linear-quadratic-Gaussian control problem with a CVaR objective, these results may be interesting in broader settings.

q-fin.TR↗

arXiv2021

Thompson Sampling with Information Relaxation Penalties

We consider a finite-horizon multi-armed bandit (MAB) problem in a Bayesian setting, for which we propose an information relaxation sampling framework. With this framework, we define an intuitive family of control policies that include Thompson sampling (TS) and the Bayesian optimal policy as endpoints. Analogous to TS, which, at each decision epoch pulls an arm that is best with respect to the randomly sampled parameters, our algorithms sample entire future reward realizations and take the corresponding best action. However, this is done in the presence of "penalties" that seek to compensate for the availability of future information. We develop several novel policies and performance bounds for MAB problems that vary in terms of improving performance and increasing computational complexity between the two endpoints. Our policies can be viewed as natural generalizations of TS that simultaneously incorporate knowledge of the time horizon and explicitly consider the exploration-exploitation trade-off. We prove associated structural results on performance bounds and suboptimality gaps. Numerical experiments suggest that this new class of policies perform well, in particular in settings where the finite time horizon introduces significant exploration-exploitation tension into the problem. Finally, inspired by the finite-horizon Gittins index, we propose an index policy that builds on our framework that particularly outperforms the state-of-the-art algorithms in our numerical experiments.

cs.LG↗

arXiv2020

Policy Gradient Optimization of Thompson Sampling Policies

We study the use of policy gradient algorithms to optimize over a class of generalized Thompson sampling policies. Our central insight is to view the posterior parameter sampled by Thompson sampling as a kind of pseudo-action. Policy gradient methods can then be tractably applied to search over a class of sampling policies, which determine a probability distribution over pseudo-actions (i.e., sampled parameters) as a function of observed data. We also propose and compare policy gradient estimators that are specialized to Bayesian bandit problems. Numerical experiments demonstrate that direct policy search on top of Thompson sampling automatically corrects for some of the algorithm's known shortcomings and offers meaningful improvements even in long horizon problems where standard Thompson sampling is extremely effective.

cs.LG↗

arXiv2018

Cross-Sectional Variation of Intraday Liquidity, Cross-Impact, and their Effect on Portfolio Execution

The composition of natural liquidity has been changing over time. An analysis of intraday volumes for the S&P500 constituent stocks illustrates that (i) volume surprises, i.e., deviations from their respective forecasts, are correlated across stocks, and (ii) this correlation increases during the last few hours of the trading session. These observations could be attributed, in part, to the prevalence of portfolio trading activity that is implicit in the growth of ETF, passive and systematic investment strategies; and, to the increased trading intensity of such strategies towards the end of the trading session, e.g., due to execution of mutual fund inflows/outflows that are benchmarked to the closing price on each day. In this paper, we investigate the consequences of such portfolio liquidity on price impact and portfolio execution. We derive a linear cross-asset market impact from a stylized model that explicitly captures the fact that a certain fraction of natural liquidity providers only trade portfolios of stocks whenever they choose to execute. We find that due to cross-impact and its intraday variation, it is optimal for a risk-neutral, cost minimizing liquidator to execute a portfolio of orders in a coupled manner, as opposed to a separable VWAP-like execution that is often assumed. The optimal schedule couples the execution of the various orders so as to be able to take advantage of increased portfolio liquidity towards the end of the day. A worst case analysis shows that the potential cost reduction from this optimized execution schedule over the separable approach can be as high as 6% for plausible model parameters. Finally, we discuss how to estimate cross-sectional price impact if one had a dataset of realized portfolio transaction records that exploits the low-rank structure of its coefficient matrix suggested by our analysis.

q-fin.TR↗