A key challenge in sequential decision problems is to determine how many samples are needed for an agent to make reliable decisions with good probabilistic guarantees. We introduce Hoeffding-like concentration inequalities that hold for a random, adaptively chosen number of samples. Our inequalities are tight under natural assumptions and can greatly simplify the analysis of common sequential decision problems. In particular, we apply them to sequential hypothesis testing, best arm identification, and sorting. The resulting algorithms rival or exceed the state of the art both theoretically and empirically.

A key challenge in sequential decision problems is to determine how many samples are needed for an agent to make reliable decisions with good probabilistic guarantees. We introduce Hoeffding-like concentration inequalities that hold for a random, adaptively chosen number of samples. Our inequalities are tight under natural assumptions and can greatly simplify the analysis of common sequential decision problems. In particular, we apply them to sequential hypothesis testing, best arm identification, and sorting. The resulting algorithms rival or exceed the state of the art both theoretically and empirically.

A key challenge in sequential decision problems is to determine how many samples are needed for an agent to make reliable decisions with good probabilistic guarantees. We introduce Hoeffding-like concentration inequalities that hold for a random, adaptively chosen number of samples. Our inequalities are tight under natural assumptions and can greatly simplify the analysis of common sequential decision problems. In particular, we apply them to sequential hypothesis testing, best arm identification, and sorting. The resulting algorithms rival or exceed the state of the art both theoretically and empirically.

As machine learning systems are increasingly used to make real world legal and financial decisions, it is of paramount importance that we develop algorithms to verify that these systems do not discriminate against minorities. We design a scalable algorithm for verifying fairness specifications. Our algorithm obtains strong correctness guarantees based on adaptive concentration inequalities; such inequalities enable our algorithm to adaptively take samples until it has enough data to make a decision. We implement our algorithm in a tool called VeriFair, and show that it scales to large machine learning models, including a deep recurrent neural network that is more than five orders of magnitude larger than the largest previously-verified neural network. While our technique only gives probabilistic guarantees due to the use of random samples, we show that we can choose the probability of error to be extremely small.

A key challenge in sequential decision problems is to determine how many samples are needed for an agent to make reliable decisions with good probabilistic guarantees. We introduce Hoeffding-like concentration inequalities that hold for a random, adaptively chosen number of samples. Our inequalities are tight under natural assumptions and can greatly simplify the analysis of common sequential decision problems. In particular, we apply them to sequential hypothesis testing, best arm identification, and sorting. The resulting algorithms rival or exceed the state of the art both theoretically and empirically.