He works on the mathematical foundations of machine learning and AI. Sham's thesis helped in laying the statistical foundations of reinforcement learning. With his collaborators, his additional contributions include: one of the first provably efficient policy search methods, Conservative Policy Iteration, for reinforcement learning; developing the mathematical foundations for the widely used linear bandit models and the Gaussian process bandit models; the tensor and spectral methodologies for provable estimation of latent variable models; the first sharp analysis of the perturbed gradient descent algorithm, along with the design and analysis of numerous other convex and non-convex algorithms. He is the recipient of the ICML Test of Time Award (2020), the IBM Pat Goldberg best paper award (in 2007), INFORMS Revenue Management and Pricing Prize (2014). He has been program chair for COLT 2011.