Exponential Speedups by Rerooting Levin Tree Search

Levin Tree Search (LTS) (Orseau et al., 2018) is a search algorithm for deterministic environments that uses a user-specified policy to guide the search. It comes with a formal guarantee on the number of search steps for finding a solution node that depends on the quality of the policy. In this paper, we introduce a new algorithm, called $\sqrt{\text{LTS}}$ (pronounce root-LTS), which implicitly starts an LTS search rooted at every node of the search tree. Each LTS search is assigned a rerooting weight by a (user-defined or learnt) rerooter, and the search effort is shared between all LTS searches proportionally to their weights. The rerooting mechanism implicitly decomposes the search space into subtasks, leading to significant speedups. We prove that the number of search steps that $\sqrt{\text{LTS}}$ takes is competitive with the best decomposition into subtasks, at the price of a factor that relates to the uncertainty of the rerooter. If LTS takes time $T$, in the best case with $q$ rerooting points, $\sqrt{\text{LTS}}$ only takes time $O(q\sqrt[q]{T})$. Like the policy, the rerooter can be learnt from data, and we expect $\sqrt{\text{LTS}}$ to be applicable to a wide range of domains.

Reclaiming the Source of Programmatic Policies: Programmatic versus Latent Spaces

Recent works have introduced LEAPS and HPRL, systems that learn latent spaces of domain-specific languages, which are used to define programmatic policies for partially observable Markov decision processes (POMDPs). These systems induce a latent space while optimizing losses such as the behavior loss, which aim to achieve locality in program behavior, meaning that vectors close in the latent space should correspond to similarly behaving programs. In this paper, we show that the programmatic space, induced by the domain-specific language and requiring no training, presents values for the behavior loss similar to those observed in latent spaces presented in previous work. Moreover, algorithms searching in the programmatic space significantly outperform those in LEAPS and HPRL. To explain our results, we measured the "friendliness" of the two spaces to local search algorithms. We discovered that algorithms are more likely to stop at local maxima when searching in the latent space than when searching in the programmatic space. This implies that the optimization topology of the programmatic space, induced by the reward function in conjunction with the neighborhood function, is more conducive to search than that of the latent space. This result provides an explanation for the superior performance in the programmatic space.

Unveiling Options with Neural Decomposition

In reinforcement learning, agents often learn policies for specific tasks without the ability to generalize this knowledge to related tasks. This paper introduces an algorithm that attempts to address this limitation by decomposing neural networks encoding policies for Markov Decision Processes into reusable sub-policies, which are used to synthesize temporally extended actions, or options. We consider neural networks with piecewise linear activation functions, so that they can be mapped to an equivalent tree that is similar to oblique decision trees. Since each node in such a tree serves as a function of the input of the tree, each sub-tree is a sub-policy of the main policy. We turn each of these sub-policies into options by wrapping it with while-loops of varied number of iterations. Given the large number of options, we propose a selection mechanism based on minimizing the Levin loss for a uniform policy on these options. Empirical results in two grid-world domains where exploration can be difficult confirm that our method can identify useful options, thereby accelerating the learning process on similar but different tasks.

Searching for Programmatic Policies in Semantic Spaces

Syntax-guided synthesis is commonly used to generate programs encoding policies. In this approach, the set of programs, that can be written in a domain-specific language defines the search space, and an algorithm searches within this space for programs that encode strong policies. In this paper, we propose an alternative method for synthesizing programmatic policies, where we search within an approximation of the language's semantic space. We hypothesized that searching in semantic spaces is more sample-efficient compared to syntax-based spaces. Our rationale is that the search is more efficient if the algorithm evaluates different agent behaviors as it searches through the space, a feature often missing in syntax-based spaces. This is because small changes in the syntax of a program often do not result in different agent behaviors. We define semantic spaces by learning a library of programs that present different agent behaviors. Then, we approximate the semantic space by defining a neighborhood function for local search algorithms, where we replace parts of the current candidate program with programs from the library. We evaluated our hypothesis in a real-time strategy game called MicroRTS. Empirical results support our hypothesis that searching in semantic spaces can be more sample-efficient than searching in syntax-based spaces.

Assessing the Interpretability of Programmatic Policies with Large Language Models

Although the synthesis of programs encoding policies often carries the promise of interpretability, systematic evaluations to assess the interpretability of these policies were never performed, likely because of the complexity of such an evaluation. In this paper, we introduce a novel metric that uses large-language models (LLM) to assess the interpretability of programmatic policies. For our metric, an LLM is given both a program and a description of its associated programming language. The LLM then formulates a natural language explanation of the program. This explanation is subsequently fed into a second LLM, which tries to reconstruct the program from the natural language explanation. Our metric measures the behavioral similarity between the reconstructed program and the original. We validate our approach using obfuscated programs that are used to solve classic programming problems. We also assess our metric with programmatic policies synthesized for playing a real-time strategy game, comparing the interpretability scores of programmatic policies synthesized by an existing system to lightly obfuscated versions of the same programs. Our LLM-based interpretability score consistently ranks less interpretable programs lower and more interpretable ones higher. These findings suggest that our metric could serve as a reliable and inexpensive tool for evaluating the interpretability of programmatic policies.

Program Synthesis with Best-First Bottom-Up Search

Cost-guided bottom-up search (BUS) algorithms use a cost function to guide the search to solve program synthesis tasks. In this paper, we show that current state-of-the-art cost-guided BUS algorithms suffer from a common problem: they can lose useful information given by the model and fail to perform the search in a best-first order according to a cost function. We introduce a novel best-first bottom-up search algorithm, which we call Bee Search, that does not suffer information loss and is able to perform cost-guided bottom-up synthesis in a best-first manner. Importantly, Bee Search performs best-first search with respect to the generation of programs, i.e., it does not even create in memory programs that are more expensive than the solution program. It attains best-first ordering with respect to generation by performing a search in an abstract space of program costs. We also introduce a new cost function that better uses the information provided by an existing cost model. Empirical results on string manipulation and bit-vector tasks show that Bee Search can outperform existing cost-guided BUS approaches when employing more complex domain-specific languages (DSLs); Bee Search and previous approaches perform equally well with simpler DSLs. Furthermore, our new cost function with Bee Search outperforms previous cost functions on string manipulation tasks.

Synthesizing Programmatic Policies with Actor-Critic Algorithms and ReLU Networks

Programmatically Interpretable Reinforcement Learning (PIRL) encodes policies in human-readable computer programs. Novel algorithms were recently introduced with the goal of handling the lack of gradient signal to guide the search in the space of programmatic policies. Most of such PIRL algorithms first train a neural policy that is used as an oracle to guide the search in the programmatic space. In this paper, we show that such PIRL-specific algorithms are not needed, depending on the language used to encode the programmatic policies. This is because one can use actor-critic algorithms to directly obtain a programmatic policy. We use a connection between ReLU neural networks and oblique decision trees to translate the policy learned with actor-critic algorithms into programmatic policies. This translation from ReLU networks allows us to synthesize policies encoded in programs with if-then-else structures, linear transformations of the input values, and PID operations. Empirical results on several control problems show that this translation approach is capable of learning short and effective policies. Moreover, the translated policies are at least competitive and often far superior to the policies PIRL algorithms synthesize.

Choosing Well Your Opponents: How to Guide the Synthesis of Programmatic Strategies

This paper introduces Local Learner (2L), an algorithm for providing a set of reference strategies to guide the search for programmatic strategies in two-player zero-sum games. Previous learning algorithms, such as Iterated Best Response (IBR), Fictitious Play (FP), and Double-Oracle (DO), can be computationally expensive or miss important information for guiding search algorithms. 2L actively selects a set of reference strategies to improve the search signal. We empirically demonstrate the advantages of our approach while guiding a local search algorithm for synthesizing strategies in three games, including MicroRTS, a challenging real-time strategy game. Results show that 2L learns reference strategies that provide a stronger search signal than IBR, FP, and DO. We also simulate a tournament of MicroRTS, where a synthesizer using 2L outperformed the winners of the two latest MicroRTS competitions, which were programmatic strategies written by human programmers.

Can You Improve My Code? Optimizing Programs with Local Search

This paper introduces a local search method for improving an existing program with respect to a measurable objective. Program Optimization with Locally Improving Search (POLIS) exploits the structure of a program, defined by its lines. POLIS improves a single line of the program while keeping the remaining lines fixed, using existing brute-force synthesis algorithms, and continues iterating until it is unable to improve the program's performance. POLIS was evaluated with a 27-person user study, where participants wrote programs attempting to maximize the score of two single-agent games: Lunar Lander and Highway. POLIS was able to substantially improve the participants' programs with respect to the game scores. A proof-of-concept demonstration on existing Stack Overflow code measures applicability in real-world problems. These results suggest that POLIS could be used as a helpful programming assistant for programming problems with measurable objectives.

Levin Tree Search with Context Models

Levin Tree Search (LTS) is a search algorithm that makes use of a policy (a probability distribution over actions) and comes with a theoretical guarantee on the number of expansions before reaching a goal node, depending on the quality of the policy. This guarantee can be used as a loss function, which we call the LTS loss, to optimize neural networks representing the policy (LTS+NN). In this work we show that the neural network can be substituted with parameterized context models originating from the online compression literature (LTS+CM). We show that the LTS loss is convex under this new model, which allows for using standard convex optimization tools, and obtain convergence guarantees to the optimal parameters in an online setting for a given set of solution trajectories -- guarantees that cannot be provided for neural networks. The new LTS+CM algorithm compares favorably against LTS+NN on several benchmarks: Sokoban (Boxoban), The Witness, and the 24-Sliding Tile puzzle (STP). The difference is particularly large on STP, where LTS+NN fails to solve most of the test instances while LTS+CM solves each test instance in a fraction of a second. Furthermore, we show that LTS+CM is able to learn a policy that solves the Rubik's cube in only a few hundred expansions, which considerably improves upon previous machine learning techniques.