Common Information Approach for Static Team Problems with Polish Spaces and Existence of Optimal Policies

In this paper, we demonstrate the existence of team-optimal strategies for static teams under observation-sharing information structures. Assuming that agents can access shared observations, we begin by converting the team problem into an equivalent centralized stochastic control problem through the introduction of a topology on policies. We subsequently apply conventional methods from stochastic control to prove the existence of team-optimal strategies. This study expands upon the widely recognized common information approach for team problems, originally designed for discrete scenarios, and adapts it to a more abstract continuous framework. The primary difficulty in this context is to establish the appropriate topology on policies.Comment: arXiv admin note: text overlap with arXiv:1711.0063

Randomized Quantization and Source Coding with Constrained Output Distribution

This paper studies fixed-rate randomized vector quantization under the constraint that the quantizer's output has a given fixed probability distribution. A general representation of randomized quantizers that includes the common models in the literature is introduced via appropriate mixtures of joint probability measures on the product of the source and reproduction alphabets. Using this representation and results from optimal transport theory, the existence of an optimal (minimum distortion) randomized quantizer having a given output distribution is shown under various conditions. For sources with densities and the mean square distortion measure, it is shown that this optimum can be attained by randomizing quantizers having convex codecells. For stationary and memoryless source and output distributions a rate-distortion theorem is proved, providing a single-letter expression for the optimum distortion in the limit of large block-lengths.Comment: To appear in the IEEE Transactions on Information Theor