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The problem of robust binary hypothesis testing is studied. Under bothhypotheses, the data-generating distributions are assumed to belong touncertainty sets constructed through moments; in particular, the sets containdistributions whose moments are centered around the empirical moments obtainedfrom training samples. The goal is to design a test that performs well underall distributions in the uncertainty sets, i.e., minimize the worst-case errorprobability over the uncertainty sets. In the finite-alphabet case, the optimaltest is obtained. In the infinite-alphabet case, a tractable approximation tothe worst-case error is derived that converges to the optimal value usingfinite samples from the alphabet. A test is further constructed to generalizeto the entire alphabet. An exponentially consistent test for testing batchsamples is also proposed. Numerical results are provided to demonstrate theperformance of the proposed robust tests.

Robust Multi-Hypothesis Testing with Moment Constrained Uncertainty Sets