Towards minimax optimal algorithms for Active Simple Hypothesis Testing

We study the problem of Active Simple Hypothesis Testing (ASHT) whe re an agent is faced with the problem of choosing between m different simple hypotheses after observing T samples. At the end of T samples, it has to output one of the m hypothesis. The distinguishing difference from the usual hypothes is testing scenario is the ability to choose one of K actions and observe the corresponding sample for that action. Th is ability to control the samples in this way makes the problem more interesting and difficult compared to the usual hypothesis testing with no control over the sample generation. The performance of the agent is meas ured in terms of the error probability its decision incurs. The above theoretical problem is a model for many practica l scenarios-A cosmetic drug trial often involve a testing period where the outcome of interest is to identify the best product after the trial period, choosing a channel from a set of channels before commencing communications, placeme nt of sensors in certain set of positions so as to minimize signal error. Any situation which require a period of testing b efore committing to a final decision with only certain fixed budget of samples (that is an inability to request additio nal samples) can be modeled effectively using ASHT and its more general version - Fixed Budget Best Arm Identific ation (FB-BAI). We intend to study the ASHT problem in the large deviation setting with the quantity of interest being the minimax error exponent over the hypotheses, that is, the worst case er ror exponent over the hypotheses.