Rahul Singh

Victor Chernozhukov, Whitney Newey, Rahul Singh et al.

We extend the idea of automated debiased machine learning to the dynamic treatment regime and more generally to nested functionals. We show that the multiply robust formula for the dynamic treatment regime with discrete treatments can be re-stated in terms of a recursive Riesz representer characterization of nested mean regressions. We then apply a recursive Riesz representer estimation learning algorithm that estimates de-biasing corrections without the need to characterize how the correction terms look like, such as for instance, products of inverse probability weighting terms, as is done in prior work on doubly robust estimation in the dynamic regime. Our approach defines a sequence of loss minimization problems, whose minimizers are the mulitpliers of the de-biasing correction, hence circumventing the need for solving auxiliary propensity models and directly optimizing for the mean squared error of the target de-biasing correction. We provide further applications of our approach to estimation of dynamic discrete choice models and estimation of long-term effects with surrogates.

Guojun Xiong, Shufan Wang, Jian Li et al.

We consider the problem of content caching at the wireless edge to serve a set of end users via unreliable wireless channels so as to minimize the average latency experienced by end users due to the constrained wireless edge cache capacity. We formulate this problem as a Markov decision process, or more specifically a restless multi-armed bandit problem, which is provably hard to solve. We begin by investigating a discounted counterpart, and prove that it admits an optimal policy of the threshold-type. We then show that this result also holds for average latency problem. Using this structural result, we establish the indexability of our problem, and employ the Whittle index policy to minimize average latency. Since system parameters such as content request rates and wireless channel conditions are often unknown and time-varying, we further develop a model-free reinforcement learning algorithm dubbed as Q^{+}-Whittle that relies on Whittle index policy. However, Q^{+}-Whittle requires to store the Q-function values for all state-action pairs, the number of which can be extremely large for wireless edge caching. To this end, we approximate the Q-function by a parameterized function class with a much smaller dimension, and further design a Q^{+}-Whittle algorithm with linear function approximation, which is called Q^{+}-Whittle-LFA. We provide a finite-time bound on the mean-square error of Q^{+}-Whittle-LFA. Simulation results using real traces demonstrate that Q^{+}-Whittle-LFA yields excellent empirical performance.