Prakirt Raj Jhunjhunwala

Jing Dong, Prakirt Raj Jhunjhunwala, Yash Kanoria

We model the interaction between a user and an AI driven recommendation system. The user initiates the process by conveying preference information through a costly and noisy message. The AI assistant, acting as a Bayesian agent, interprets the user's message to form a posterior belief about their true preferences and make product recommendations. In particular, it determines how many recommendations to present so as to maximize the user's expected utility from their final choice, while accounting for the search cost induced by the size of the recommendation set. We use mutual information based cost functions to model the two distinct costs incurred by the user during the interaction: (i) a communication cost, which increases with the precision of their preference message, and (ii) a search cost, which increases with the size of the recommendation set provided by the AI assistant. We study products and preferences which live in d dimensional space, and ask how the user's expected payoff can be maximized. For large d, we characterize how optimal message precision and recommendation set size depend on the cost parameters, under two distinct distributions from which recommendations can be sampled from the product universe: (i) Bayes' posterior belief, and (ii) an optimized tilted distribution. Under the posterior sampling scheme (i), we identify a hybrid regime, in which an efficient interaction policy requires jointly optimizing the amount of information (in bits) conveyed by the user and the number of recommendations provided by the AI assistant. In the tilted sampling scheme (ii), our results show that the optimal interaction policy uses only one of communication and search, favoring whichever of them is less costly.

Sajad Khodadadian, Prakirt Raj Jhunjhunwala, Sushil Mahavir Varma et al.

Markov Decision Processes are classically solved using Value Iteration and Policy Iteration algorithms. Recent interest in Reinforcement Learning has motivated the study of methods inspired by optimization, such as gradient ascent. Among these, a popular algorithm is the Natural Policy Gradient, which is a mirror descent variant for MDPs. This algorithm forms the basis of several popular Reinforcement Learning algorithms such as Natural actor-critic, TRPO, PPO, etc, and so is being studied with growing interest. It has been shown that Natural Policy Gradient with constant step size converges with a sublinear rate of O(1/k) to the global optimal. In this paper, we present improved finite time convergence bounds, and show that this algorithm has geometric (also known as linear) asymptotic convergence rate. We further improve this convergence result by introducing a variant of Natural Policy Gradient with adaptive step sizes. Finally, we compare different variants of policy gradient methods experimentally.