INT: An Inequality Benchmark for Evaluating Generalization in Theorem Proving

In learning-assisted theorem proving, one of the most critical challenges is to generalize to theorems unlike those seen at training time. In this paper, we introduce INT, an INequality Theorem proving benchmark, specifically designed to test agents' generalization ability. INT is based on a procedure for generating theorems and proofs; this procedure's knobs allow us to measure 6 different types of generalization, each reflecting a distinct challenge characteristic to automated theorem proving. In addition, unlike prior benchmarks for learning-assisted theorem proving, INT provides a lightweight and user-friendly theorem proving environment with fast simulations, conducive to performing learning-based and search-based research. We introduce learning-based baselines and evaluate them across 6 dimensions of generalization with the benchmark. We then evaluate the same agents augmented with Monte Carlo Tree Search (MCTS) at test time, and show that MCTS can help to prove new theorems.

Using Social Networks to Aid Homeless Shelters: Dynamic Influence Maximization under Uncertainty - An Extended Version

This paper presents HEALER, a software agent that recommends sequential intervention plans for use by homeless shelters, who organize these interventions to raise awareness about HIV among homeless youth. HEALER's sequential plans (built using knowledge of social networks of homeless youth) choose intervention participants strategically to maximize influence spread, while reasoning about uncertainties in the network. While previous work presents influence maximizing techniques to choose intervention participants, they do not address three real-world issues: (i) they completely fail to scale up to real-world sizes; (ii) they do not handle deviations in execution of intervention plans; (iii) constructing real-world social networks is an expensive process. HEALER handles these issues via four major contributions: (i) HEALER casts this influence maximization problem as a POMDP and solves it using a novel planner which scales up to previously unsolvable real-world sizes; (ii) HEALER allows shelter officials to modify its recommendations, and updates its future plans in a deviation-tolerant manner; (iii) HEALER constructs social networks of homeless youth at low cost, using a Facebook application. Finally, (iv) we show hardness results for the problem that HEALER solves. HEALER will be deployed in the real world in early Spring 2016 and is currently undergoing testing at a homeless shelter.