Cong Shi

Daniele Bracale, Moulinath Banerjee, Cong Shi et al.

We study a sequential price competition among $N$ sellers, each influenced by the pricing decisions of their rivals. Specifically, the demand function for each seller $i$ follows the single index model $λ_i(\mathbf p) = μ_i(\langle \boldsymbol θ_{i,0}, \mathbf p \rangle)$, with known increasing link $μ_i$ and unknown parameter $\boldsymbol θ_{i,0}$, where the vector $\mathbf{p}$ denotes the vector of prices offered by all the sellers simultaneously at a given instant. Each seller observes only their own realized demand - unobservable to competitors - and the prices set by rivals. We propose a novel decentralized policy, PML-GLUCB, that combines penalized MLE with an upper-confidence pricing rule. Our approach (i) \emph{removes the need for coordinated front-loaded exploration phases across sellers} - which is integral to previous models - making our method aligned with realistic market conditions; (ii) generalizes existing approaches that focus solely on linear demand models; (iii) accommodates both binary and real-valued demand observations. Relative to a dynamic benchmark policy, each seller achieves $\widetilde{O}(\sqrt{T})$ regret, which matches the optimal rate known in the linear setting.

Daniele Bracale, Moulinath Banerjee, Cong Shi et al.

We consider price competition among multiple sellers over a selling horizon of $T$ periods. In each period, sellers simultaneously offer their prices (which are made public) and subsequently observe their respective demand (not made public). The demand function of each seller depends on all sellers' prices through a private, unknown, and nonlinear relationship. We propose a dynamic pricing policy that uses semi-parametric least-squares estimation and show that when the sellers employ our policy, their prices converge at a rate of $O(T^{-1/7})$ to the Nash equilibrium prices that sellers would reach if they were fully informed. Each seller incurs a regret of $O(T^{5/7})$ relative to a dynamic benchmark policy. A theoretical contribution of our work is proving the existence of equilibrium under shape-constrained demand functions via the concept of $s$-concavity and establishing regret bounds of our proposed policy. Technically, we also establish new concentration results for the least squares estimator under shape constraints. Our findings offer significant insights into dynamic competition-aware pricing and contribute to the broader study of non-parametric learning in strategic decision-making.

Zeyu Bian, Zhengling Qi, Cong Shi et al.

This paper studies offline dynamic pricing without data coverage assumption, thereby allowing for any price including the optimal one not being observed in the offline data. Previous approaches that rely on the various coverage assumptions such as that the optimal prices are observable, would lead to suboptimal decisions and consequently, reduced profits. We address this challenge by framing the problem to a partial identification framework. Specifically, we establish a partial identification bound for the demand parameter whose associated price is unobserved by leveraging the inherent monotonicity property in the pricing problem. We further incorporate pessimistic and opportunistic strategies within the proposed partial identification framework to derive the estimated policy. Theoretically, we establish rate-optimal finite-sample regret guarantees for both strategies. Empirically, we demonstrate the superior performance of the newly proposed methods via a synthetic environment. This research provides practitioners with valuable insights into offline pricing strategies in the challenging no-coverage setting, ultimately fostering sustainable growth and profitability of the company.

Leon Frischauf, Otmar Scherzer, Cong Shi

Neural networks with quadratic decision functions have been introduced as alternatives to standard neural networks with affine linear ones. They are advantageous when the objects or classes to be identified are compact and of basic geometries like circles, ellipses etc. In this paper we investigate the use of such ansatz functions for classification. In particular we test and compare the algorithm on the MNIST dataset for classification of handwritten digits and for classification of subspecies. We also show, that the implementation can be based on the neural network structure in the software Tensorflow and Keras, respectively.

Yaohui Guo, Cong Shi, X. Jessie Yang

To facilitate effective human-robot interaction (HRI), trust-aware HRI has been proposed, wherein the robotic agent explicitly considers the human's trust during its planning and decision making. The success of trust-aware HRI depends on the specification of a trust dynamics model and a trust-behavior model. In this study, we proposed one novel trust-behavior model, namely the reverse psychology model, and compared it against the commonly used disuse model. We examined how the two models affect the robot's optimal policy and the human-robot team performance. Results indicate that the robot will deliberately "manipulate" the human's trust under the reverse psychology model. To correct this "manipulative" behavior, we proposed a trust-seeking reward function that facilitates trust establishment without significantly sacrificing the team performance.