He Wang

Shixiang Zhu, He Wang, Yao Xie

We present a data-driven optimization framework for redesigning police patrol zones in an urban environment. The objectives are to rebalance police workload among geographical areas and to reduce response time to emergency calls. We develop a stochastic model for police emergency response by integrating multiple data sources, including police incidents reports, demographic surveys, and traffic data. Using this stochastic model, we optimize zone redesign plans using mixed-integer linear programming. Our proposed design was implemented by the Atlanta Police Department in March 2019. By analyzing data before and after the zone redesign, we show that the new design has reduced the response time to high priority 911 calls by 5.8\% and the imbalance of police workload among different zones by 43\%.

Yining Wang, He Wang

Price-based revenue management is an important problem in operations management with many practical applications. The problem considers a retailer who sells a product (or multiple products) over $T$ consecutive time periods and is subject to constraints on the initial inventory levels. While the optimal pricing policy could be obtained via dynamic programming, such an approach is sometimes undesirable because of high computational costs. Approximate policies, such as the re-solving heuristics, are often applied as computationally tractable alternatives. In this paper, we show the following two results. First, we prove that a natural re-solving heuristic attains $O(1)$ regret compared to the value of the optimal policy. This improves the $O(\ln T)$ regret upper bound established in the prior work of \cite{jasin2014reoptimization}. Second, we prove that there is an $Ω(\ln T)$ gap between the value of the optimal policy and that of the fluid model. This complements our upper bound result by showing that the fluid is not an adequate information-relaxed benchmark when analyzing price-based revenue management algorithms.

Adrian Rivera Cardoso, Jacob Abernethy, He Wang et al.

We study the problem of repeated play in a zero-sum game in which the payoff matrix may change, in a possibly adversarial fashion, on each round; we call these Online Matrix Games. Finding the Nash Equilibrium (NE) of a two player zero-sum game is core to many problems in statistics, optimization, and economics, and for a fixed game matrix this can be easily reduced to solving a linear program. But when the payoff matrix evolves over time our goal is to find a sequential algorithm that can compete with, in a certain sense, the NE of the long-term-averaged payoff matrix. We design an algorithm with small NE regret--that is, we ensure that the long-term payoff of both players is close to minimax optimum in hindsight. Our algorithm achieves near-optimal dependence with respect to the number of rounds and depends poly-logarithmically on the number of available actions of the players. Additionally, we show that the naive reduction, where each player simply minimizes its own regret, fails to achieve the stated objective regardless of which algorithm is used. We also consider the so-called bandit setting, where the feedback is significantly limited, and we provide an algorithm with small NE regret using one-point estimates of each payoff matrix.

Adrian Rivera Cardoso, He Wang, Huan Xu

We consider Markov Decision Processes (MDPs) where the rewards are unknown and may change in an adversarial manner. We provide an algorithm that achieves state-of-the-art regret bound of $O( \sqrt{τ(\ln|S|+\ln|A|)T}\ln(T))$, where $S$ is the state space, $A$ is the action space, $τ$ is the mixing time of the MDP, and $T$ is the number of periods. The algorithm's computational complexity is polynomial in $|S|$ and $|A|$ per period. We then consider a setting often encountered in practice, where the state space of the MDP is too large to allow for exact solutions. By approximating the state-action occupancy measures with a linear architecture of dimension $d\ll|S|$, we propose a modified algorithm with computational complexity polynomial in $d$. We also prove a regret bound for this modified algorithm, which to the best of our knowledge this is the first $\tilde{O}(\sqrt{T})$ regret bound for large scale MDPs with changing rewards.

Adrian Rivera, He Wang, Huan Xu

We study the online saddle point problem, an online learning problem where at each iteration a pair of actions need to be chosen without knowledge of the current and future (convex-concave) payoff functions. The objective is to minimize the gap between the cumulative payoffs and the saddle point value of the aggregate payoff function, which we measure using a metric called "SP-Regret". The problem generalizes the online convex optimization framework but here we must ensure both players incur cumulative payoffs close to that of the Nash equilibrium of the sum of the games. We propose an algorithm that achieves SP-Regret proportional to $\sqrt{\ln(T)T}$ in the general case, and $\log(T)$ SP-Regret for the strongly convex-concave case. We also consider the special case where the payoff functions are bilinear and the decision sets are the probability simplex. In this setting we are able to design algorithms that reduce the bounds on SP-Regret from a linear dependence in the dimension of the problem to a \textit{logarithmic} one. We also study the problem under bandit feedback and provide an algorithm that achieves sublinear SP-Regret. We then consider an online convex optimization with knapsacks problem motivated by a wide variety of applications such as: dynamic pricing, auctions, and crowdsourcing. We relate this problem to the online saddle point problem and establish $O(\sqrt{T})$ regret using a primal-dual algorithm.