Learning Admissible Heuristics for A*: Theory and Practice

Heuristic functions are central to the performance of search algorithms such as A-star, where admissibility - the property of never overestimating the true shortest-path cost - guarantees solution optimality. Recent deep learning approaches often disregard admissibility and provide limited guarantees on generalization beyond the training data. This paper addresses both of these limitations. First, we pose heuristic learning as a constrained optimization problem and introduce Cross-Entropy Admissibility (CEA), a loss function that enforces admissibility during training. On the Rubik's Cube domain, this method yields near-admissible heuristics with significantly stronger guidance than compressed pattern database (PDB) heuristics. Theoretically, we study the sample complexity of learning heuristics. By leveraging PDB abstractions and the structural properties of graphs such as the Rubik's Cube, we tighten the bound on the number of training samples needed for A-star to generalize. Replacing a general hypothesis class with a ReLU neural network gives bounds that depend primarily on the network's width and depth, rather than on graph size. Using the same network, we also provide the first generalization guarantees for goal-dependent heuristics.

A Parallel CPU-GPU Framework for Cost-Bounded DFS with Applications to IDA* and BTS

The rapid advancement of GPU technology has unlocked powerful parallel processing capabilities, creating new opportunities to enhance classic search algorithms. A recent successful application of GPUs is in compressing large pattern database (PDB) heuristics using neural networks while preserving heuristic admissibility. However, very few algorithms have been designed to exploit GPUs during search. Several variants of A* exist that batch GPU computations. In this paper we introduce a method for batching GPU computations in depth first search. In particular, we describe a new cost-bounded depth-first search (CB-DFS) method that leverages the combined parallelism of modern CPUs and GPUs. This is used to create algorithms like \emph{Batch IDA*}, an extension of the Iterative Deepening A* (IDA*) algorithm, or Batch BTS, an extensions of Budgeted Tree Search. Our approach builds on the general approach used by Asynchronous Parallel IDA* (AIDA*), while maintaining optimality guarantees. We evaluate the approach on the 3x3 Rubik's Cube and 4x4 sliding tile puzzle (STP), showing that GPU operations can be efficiently batched in DFS. Additionally, we conduct extensive experiments to analyze the effects of hyperparameters, neural network heuristic size, and hardware resources on performance.

ETGL-DDPG: A Deep Deterministic Policy Gradient Algorithm for Sparse Reward Continuous Control

We consider deep deterministic policy gradient (DDPG) in the context of reinforcement learning with sparse rewards. To enhance exploration, we introduce a search procedure, \emph{${\epsilon}{t}$-greedy}, which generates exploratory options for exploring less-visited states. We prove that search using $\epsilon t$-greedy has polynomial sample complexity under mild MDP assumptions. To more efficiently use the information provided by rewarded transitions, we develop a new dual experience replay buffer framework, \emph{GDRB}, and implement \emph{longest n-step returns}. The resulting algorithm, \emph{ETGL-DDPG}, integrates all three techniques: \bm{$\epsilon t$}-greedy, \textbf{G}DRB, and \textbf{L}ongest $n$-step, into DDPG. We evaluate ETGL-DDPG on standard benchmarks and demonstrate that it outperforms DDPG, as well as other state-of-the-art methods, across all tested sparse-reward continuous environments. Ablation studies further highlight how each strategy individually enhances the performance of DDPG in this setting.