Heuristic search algorithms are widely used in both AI planning and the decoding of sequences from deep neural networks. In recent years, several lines of work have highlighted different factors that impact the empirical performance of heuristic search algorithms. However, a principled empirical understanding of the search behavior of these heuristic search algorithms has yet to be developed.

Empirical models, such as the phase transition and the heavy-tailed behavior, have been central to the development of empirical understanding of combinatorial search problems such as constraint satisfaction problems (CSP) and satisfiability (SAT). In this dissertation, we investigate the use of empirical models to explain the behavior of heuristic search algorithms in AI planning and neural sequence decoding and support the development of more efficient search algorithms.

In AI planning, we develop empirical models for problem difficulty of greedy best first (GBFS), the most commonly used algorithm for satisficing planning. First, we establish the existence of a phase transition in the solubility of planning problems and investigate its implications to problem difficulty. Then, we demonstrate the heavy-tailed behavior of GBFS and provide a deeper understanding of the connection between constrainedness and local minima. Informed by our analysis, we develop a novel variant of GBFS that outperforms the baseline.

In neural sequence decoding, we develop empirical models for the performance of beam search, the ubiquitous algorithm for decoding deep sequence models. First, we investigate the empirical problem of performance degradation in beam search. We present an explanatory model based on search discrepancies that generalizes previous observations on the behavior of beam search. Building on our analysis, we present two heuristic techniques that eliminate the problem. Next, we study goal-oriented sequence decoding and show that, similar to GBFS, we observe heavy-tailed behavior. We present a novel variant of goal-oriented beam search that exploits our insights and outperforms the baseline.

Our work shows the importance of empirical models in the study and development of heuristic search algorithms and demonstrates that empirical models developed for CSPs and SAT can be adapted to AI planning and neural sequence decoding.