Common Benchmarks Undervalue the Generalization Power of Programmatic Policies

Algorithms for learning programmatic representations for sequential decision-making problems are often evaluated on out-of-distribution (OOD) problems, with the common conclusion that programmatic policies generalize better than neural policies on OOD problems. In this position paper, we argue that commonly used benchmarks undervalue the generalization capabilities of programmatic representations. We analyze the experiments of four papers from the literature and show that neural policies, which were shown not to generalize, can generalize as effectively as programmatic policies on OOD problems. This is achieved with simple changes in the neural policies training pipeline. Namely, we show that simpler neural architectures with the same type of sparse observation used with programmatic policies can help attain OOD generalization. Another modification we have shown to be effective is the use of reward functions that allow for safer policies (e.g., agents that drive slowly can generalize better). Also, we argue for creating benchmark problems highlighting concepts needed for OOD generalization that may challenge neural policies but align with programmatic representations, such as tasks requiring algorithmic constructs like stacks.

Subgoal-Guided Policy Heuristic Search with Learned Subgoals

Policy tree search is a family of tree search algorithms that use a policy to guide the search. These algorithms provide guarantees on the number of expansions required to solve a given problem that are based on the quality of the policy. While these algorithms have shown promising results, the process in which they are trained requires complete solution trajectories to train the policy. Search trajectories are obtained during a trial-and-error search process. When the training problem instances are hard, learning can be prohibitively costly, especially when starting from a randomly initialized policy. As a result, search samples are wasted in failed attempts to solve these hard instances. This paper introduces a novel method for learning subgoal-based policies for policy tree search algorithms. The subgoals and policies conditioned on subgoals are learned from the trees that the search expands while attempting to solve problems, including the search trees of failed attempts. We empirically show that our policy formulation and training method improve the sample efficiency of learning a policy and heuristic function in this online setting.

InnateCoder: Learning Programmatic Options with Foundation Models

Outside of transfer learning settings, reinforcement learning agents start their learning process from a clean slate. As a result, such agents have to go through a slow process to learn even the most obvious skills required to solve a problem. In this paper, we present InnateCoder, a system that leverages human knowledge encoded in foundation models to provide programmatic policies that encode "innate skills" in the form of temporally extended actions, or options. In contrast to existing approaches to learning options, InnateCoder learns them from the general human knowledge encoded in foundation models in a zero-shot setting, and not from the knowledge the agent gains by interacting with the environment. Then, InnateCoder searches for a programmatic policy by combining the programs encoding these options into larger and more complex programs. We hypothesized that InnateCoder's way of learning and using options could improve the sampling efficiency of current methods for learning programmatic policies. Empirical results in MicroRTS and Karel the Robot support our hypothesis, since they show that InnateCoder is more sample efficient than versions of the system that do not use options or learn them from experience.

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.