Explaining and reasoning about processes which underlie observed black-box phenomena enables the discovery of causal mechanisms, derivation of suitable abstract representations and the formulation of more robust predictions. We propose to learn high level functional programs in order to represent abstract models which capture the invariant structure in the observed data. We introduce the @math -machine (program-induction machine) -- an architecture able to induce interpretable LISP-like programs from observed data traces. We propose an optimisation procedure for program learning based on backpropagation, gradient descent and A* search. We apply the proposed method to three problems: system identification of dynamical systems, explaining the behaviour of a DQN agent and learning by demonstration in a human-robot interaction scenario. Our experimental results show that the @math -machine can efficiently induce interpretable programs from individual data traces.
Determining how many input output examples or execution traces are required in order to generalise well is still an open research problem. However, in this paper, we focus attention more on the explanatory power afforded by programs rather than on the broader problems of generalisation in the space of programs. While these characteristics are of course related, we take a view similar to that of @cite_0 , arguing that it is possible to build from locally valid program fragments which provide useful insight into the black-box processes generating the data. By combining gradient descent and A* search the @math -machine is able to learn informative and interpretable high-level LISP-like programs, even just from a single observation trace.
@cite_0
2282821441
We study machine learning formulations of inductive program synthesis; given input-output examples, we try to synthesize source code that maps inputs to corresponding outputs. Our aims are to develop new machine learning approaches based on neural networks and graphical models, and to understand the capabilities of machine learning techniques relative to traditional alternatives, such as those based on constraint solving from the programming languages community. Our key contribution is the proposal of TerpreT, a domain-specific language for expressing program synthesis problems. TerpreT is similar to a probabilistic programming language: a model is composed of a specification of a program representation (declarations of random variables) and an interpreter describing how programs map inputs to outputs (a model connecting unknowns to observations). The inference task is to observe a set of input-output examples and infer the underlying program. TerpreT has two main benefits. First, it enables rapid exploration of a range of domains, program representations, and interpreter models. Second, it separates the model specification from the inference algorithm, allowing like-to-like comparisons between different approaches to inference. From a single TerpreT specification we automatically perform inference using four different back-ends. These are based on gradient descent, linear program (LP) relaxations for graphical models, discrete satisfiability solving, and the Sketch program synthesis system. We illustrate the value of TerpreT by developing several interpreter models and performing an empirical comparison between alternative inference algorithms. Our key empirical finding is that constr