Jean Walrand

Vijay Kamble, Patrick Loiseau, Jean Walrand

We describe an approximate dynamic programming (ADP) approach to compute approximations of the optimal strategies and of the minimal losses that can be guaranteed in discounted repeated games with vector-valued losses. Such games prominently arise in the analysis of regret in repeated decision-making in adversarial environments, also known as adversarial online learning. At the core of our approach is a characterization of the lower Pareto frontier of the set of expected losses that a player can guarantee in these games as the unique fixed point of a set-valued dynamic programming operator. When applied to the problem of regret minimization with discounted losses, our approach yields algorithms that achieve markedly improved performance bounds compared to off-the-shelf online learning algorithms like Hedge. These results thus suggest the significant potential of ADP-based approaches in adversarial online learning.

Yuan Luo, Nihar B. Shah, Jianwei Huang et al.

We consider a problem of prediction based on opinions elicited from heterogeneous rational agents with private information. Making an accurate prediction with a minimal cost requires a joint design of the incentive mechanism and the prediction algorithm. Such a problem lies at the nexus of statistical learning theory and game theory, and arises in many domains such as consumer surveys and mobile crowdsourcing. In order to elicit heterogeneous agents' private information and incentivize agents with different capabilities to act in the principal's best interest, we design an optimal joint incentive mechanism and prediction algorithm called COPE (COst and Prediction Elicitation), the analysis of which offers several valuable engineering insights. First, when the costs incurred by the agents are linear in the exerted effort, COPE corresponds to a "crowd contending" mechanism, where the principal only employs the agent with the highest capability. Second, when the costs are quadratic, COPE corresponds to a "crowd-sourcing" mechanism that employs multiple agents with different capabilities at the same time. Numerical simulations show that COPE improves the principal's profit and the network profit significantly (larger than 30% in our simulations), comparing to those mechanisms that assume all agents have equal capabilities.