We present a new approach, called meta-meta classification, to learning in small-data settings. In this approach, one uses a large set of learning problems to design an ensemble of learners, where each learner has high bias and low variance and is skilled at solving a specific type of learning problem. The meta-meta classifier learns how to examine a given learning problem and combine the various learners to solve the problem. The meta-meta learning approach is especially suited to solving few-shot learning tasks, as it is easier to learn to classify a new learning problem with little data than it is to apply a learning algorithm to a small data set. We evaluate the approach on a one-shot, one-class-versus-all classification task and show that it is able to outperform traditional meta-learning as well as ensembling approaches.

We present Imitation-Projected Policy Gradient (IPPG), an algorithmic framework for learning policies that are parsimoniously represented in a structured programming language. Such programmatic policies can be more interpretable, generalizable, and amenable to formal verification than neural policies; however, designing rigorous learning approaches for programmatic policies remains a challenge. IPPG, our response to this challenge, is based on three insights. First, we view our learning task as optimization in policy space, modulo the constraint that the desired policy has a programmatic representation, and solve this optimization problem using a "lift-and-project" perspective that takes a gradient step into the unconstrained policy space and then projects back onto the constrained space. Second, we view the unconstrained policy space as mixing neural and programmatic representations, which enables employing state-of-the-art deep policy gradient approaches. Third, we cast the projection step as program synthesis via imitation learning, and exploit contemporary combinatorial methods for this task. We present theoretical convergence results for IPPG, as well as an empirical evaluation in three continuous control domains. The experiments show that IPPG can significantly outperform state-of-the-art approaches for learning programmatic policies.

Dealing with high variance is a significant challenge in model-free reinforcement learning (RL). Existing methods are unreliable, exhibiting high variance in performance from run to run using different initializations/seeds. Focusing on problems arising in continuous control, we propose a functional regularization approach to augmenting model-free RL. In particular, we regularize the behavior of the deep policy to be similar to a policy prior, i.e., we regularize in function space. We show that functional regularization yields a bias-variance trade-off, and propose an adaptive tuning strategy to optimize this trade-off. When the policy prior has control-theoretic stability guarantees, we further show that this regularization approximately preserves those stability guarantees throughout learning. We validate our approach empirically on a range of settings, and demonstrate significantly reduced variance, guaranteed dynamic stability, and more efficient learning than deep RL alone.

We present a neurosymbolic framework for the lifelong learning of algorithmic tasks that mix perception and procedural reasoning. Reusing high-level concepts across domains and learning complex procedures are key challenges in lifelong learning. We show that a program synthesis approach that combines gradient descent with combinatorial search over programs can be a more effective response to these challenges than purely neural methods. Our framework, called HOUDINI, represents neural networks as strongly typed, differentiable functional programs that use symbolic higher-order combinators to compose a library of neural functions. Our learning algorithm consists of: (1) a symbolic program synthesizer that performs a type-directed search over parameterized programs, and decides on the library functions to reuse, and the architectures to combine them, while learning a sequence of tasks; and (2) a neural module that trains these programs using stochastic gradient descent. We evaluate HOUDINI on three benchmarks that combine perception with the algorithmic tasks of counting, summing, and shortest-path computation. Our experiments show that HOUDINI transfers high-level concepts more effectively than traditional transfer learning and progressive neural networks, and that the typed representation of networks significantly accelerates the search.

We present a neurosymbolic framework for the lifelong learning of algorithmic tasks that mix perception and procedural reasoning. Reusing high-level concepts across domains and learning complex procedures are key challenges in lifelong learning. We show that a program synthesis approach that combines gradient descent with combinatorial search over programs can be a more effective response to these challenges than purely neural methods. Our framework, called HOUDINI, represents neural networks as strongly typed, differentiable functional programs that use symbolic higher-order combinators to compose a library of neural functions. Our learning algorithm consists of: (1) a symbolic program synthesizer that performs a type-directed search over parameterized programs, and decides on the library functions to reuse, and the architectures to combine them, while learning a sequence of tasks; and (2) a neural module that trains these programs using stochastic gradient descent. We evaluate HOUDINI on three benchmarks that combine perception with the algorithmic tasks of counting, summing, and shortest-path computation. Our experiments show that HOUDINI transfers high-level concepts more effectively than traditional transfer learning and progressive neural networks, and that the typed representation of networks significantly accelerates the search.

Planning robust executions under uncertainty is a fundamental challenge for building autonomous robots. Partially Observable Markov Decision Processes (POMDPs) provide a standard framework for modeling uncertainty in many applications. In this work, we study POMDPs with safe-reachability objectives, which require that with a probability above some threshold, a goal state is eventually reached while keeping the probability of visiting unsafe states below some threshold. This POMDP formulation is different from the traditional POMDP models with optimality objectives and we show that in some cases, POMDPs with safe-reachability objectives can provide a better guarantee of both safety and reachability than the existing POMDP models through an example. A key algorithmic problem for POMDPs is policy synthesis, which requires reasoning over a vast space of beliefs (probability distributions). To address this challenge, we introduce the notion of a goal-constrained belief space, which only contains beliefs reachable from the initial belief under desired executions that can achieve the given safe-reachability objective. Our method compactly represents this space over a bounded horizon using symbolic constraints, and employs an incremental Satisfiability Modulo Theories (SMT) solver to efficiently search for a valid policy over it. We evaluate our method using a case study involving a partially observable robotic domain with uncertain obstacles. The results show that our method can synthesize policies over large belief spaces with a small number of SMT solver calls by focusing on the goal-constrained belief space.

We study the problem of generating interpretable and verifiable policies through reinforcement learning. Unlike the popular Deep Reinforcement Learning (DRL) paradigm, in which the policy is represented by a neural network, the aim in Programmatically Interpretable Reinforcement Learning is to find a policy that can be represented in a high-level programming language. Such programmatic policies have the benefits of being more easily interpreted than neural networks, and being amenable to verification by symbolic methods. We propose a new method, called Neurally Directed Program Search (NDPS), for solving the challenging nonsmooth optimization problem of finding a programmatic policy with maxima reward. NDPS works by first learning a neural policy network using DRL, and then performing a local search over programmatic policies that seeks to minimize a distance from this neural "oracle". We evaluate NDPS on the task of learning to drive a simulated car in the TORCS car-racing environment. We demonstrate that NDPS is able to discover human-readable policies that pass some significant performance bars. We also find that a well-designed policy language can serve as a regularizer, and result in the discovery of policies that lead to smoother trajectories and are more easily transferred to environments not encountered during training.

We present a neurosymbolic approach to the lifelong learning of algorithmic tasks that mix perception and procedural reasoning. Reusing highlevel concepts across domains and learning complex procedures are two key challenges in lifelong learning. We show that a combination of gradientbased learning and symbolic program synthesis can be a more effective response to these challenges than purely neural methods. Concretely, our approach, called HOUDINI, represents neural networks as strongly typed, end-to-end differentiable functional programs that use symbolic higher-order combinators to compose a library of neural functions. Our learning algorithm consists of: (1) a program synthesizer that performs a type-directed search over programs in this language, and decides on the library functions that should be reused and the architectures that should be used to combine them; and (2) a neural module that trains synthesized programs using stochastic gradient descent. We evaluate our approach on three algorithmic tasks. Our experiments show that our type-directed search technique is able to significantly prune the search space of programs, and that the overall approach transfers high-level concepts more effectively than monolithic neural networks as well as traditional transfer learning.