Many methods exist for function optimization, such as randomly sampling the variable search space, called random search, or systematically evaluating samples in a grid across the search space, called grid search. More principled methods are able to learn from sampling the space so that future samples are directed toward the parts of the search space that are most likely to contain the extrema. A directed approach to global optimization that uses probability is called Bayesian Optimization. Take my free 7-day email crash course now (with sample code). Click to sign-up and also get a free PDF Ebook version of the course.

In aviation, the black box is a source of knowledge: a receptacle of crucial data that might help investigators understand catastrophe. In technology, a black box is the absence of knowledge: a catchall term describing an algorithmic system with mechanics its creators can't--or won't--explain. Algorithms, in this telling, are unknowable, uncontrollable, and independent of human oversight, even as they promote extremist content, make decisions affecting our health, or act in potential violation of antitrust law. In investigative reports and international courts, Amazon, Google, and other tech platforms have been accused of tweaking their search algorithms to boost their own profits and sidestep antitrust regulations. Each company denies interfering with its respective search algorithm, and because of the murky mechanics of how search works, proving the allegations is nearly impossible.

We show how complexity theory can be introduced in machine learning to help bring together apparently disparate areas of current research. We show that this new approach requires less training data and is more generalizable as it shows greater resilience to random attacks. We investigate the shape of the discrete algorithmic space when performing regression or classification using a loss function parametrized by algorithmic complexity, demonstrating that the property of differentiation is not necessary to achieve results similar to those obtained using differentiable programming approaches such as deep learning. In doing so we use examples which enable the two approaches to be compared (small, given the computational power required for estimations of algorithmic complexity). We find and report that (i) machine learning can successfully be performed on a non-smooth surface using algorithmic complexity; (ii) that parameter solutions can be found using an algorithmic-probability classifier, establishing a bridge between a fundamentally discrete theory of computability and a fundamentally continuous mathematical theory of optimization methods; (iii) a formulation of an algorithmically directed search technique in non-smooth manifolds can be defined and conducted; (iv) exploitation techniques and numerical methods for algorithmic search to navigate these discrete non-differentiable spaces can be performed; in application of the (a) identification of generative rules from data observations; (b) solutions to image classification problems more resilient against pixel attacks compared to neural networks; (c) identification of equation parameters from a small data-set in the presence of noise in continuous ODE system problem, (d) classification of Boolean NK networks by (1) network topology, (2) underlying Boolean function, and (3) number of incoming edges.

There are notable examples of online search improving over hand-coded or learned policies (e.g. AlphaZero) for sequential decision making. It is not clear, however, whether or not policy improvement is guaranteed for many of these approaches, even when given a perfect evaluation function and transition model. Indeed, simple counter examples show that seemingly reasonable online search procedures can hurt performance compared to the original policy. To address this issue, we introduce the choice function framework for analyzing online search procedures for policy improvement. A choice function specifies the actions to be considered at every node of a search tree, with all other actions being pruned. Our main contribution is to give sufficient conditions for stationary and non-stationary choice functions to guarantee that the value achieved by online search is no worse than the original policy. In addition, we describe a general parametric class of choice functions that satisfy those conditions and present an illustrative use case of the framework's empirical utility.

In this paper, we develop a framework to obtain graph abstractions for decision-making by an agent where the abstractions emerge as a function of the agent's limited computational resources. We discuss the connection of the proposed approach with information-theoretic signal compression, and formulate a novel optimization problem to obtain tree-based abstractions as a function of the agent's computational resources. The structural properties of the new problem are discussed in detail, and two algorithmic approaches are proposed to obtain solutions to this optimization problem. We discuss the quality of, and prove relationships between, solutions obtained by the two proposed algorithms. The framework is demonstrated to generate a hierarchy of abstractions for a non-trivial environment.

To appear at NeurIPS 2019. Modular and programmable architecture search framework that allows you to implement your own search spaces and search algorithms through a consistent API. Reading the Twitter thread will give you a pretty good idea of the main ideas. Looking to get a few initial users and feedback.

Proteins are a class of large molecules that are involved in the vast majority of biological functions, from cell replication to photosynthesis to cognition. The chemical structure of proteins is very systematic5--they consist of a chain of atoms known as the backbone, which consists of three-atom (nitrogen-carbon-carbon) repeats known as residues, each of which features a sidechain of atoms emanating from the first carbon. In general, there are 20 different options for sidechains, and a residue with a particular type of sidechain is known as an amino acid (so there are also 20 different amino acid types). For billions of years, the process of evolution has optimized the sequence of amino acids that make up naturally occurring proteins to suit the needs of the organisms that make them. So we ask: Can we use computation to design non-naturally occurring proteins that suit our biomedical and industrial needs? This question is a combinatorial optimization problem, because the output of a protein design computation is a sequence of amino acids. Due to the vast diversity of naturally occurring proteins, it is possible--and very useful--to begin a protein design computation with a naturally occurring protein and then to modify it to achieve the desired function. In this article, we focus on protein design algorithms that perform this optimization using detailed modeling of the 3D structure of the protein.5,8 Thus, they will begin with a starting structure, a 3D structure of a (typically naturally occurring) protein we wish to modify. To illustrate this concept, imagine we wish to perform a simple example modification to a protein to make it more stable, so it can still function at higher temperatures.

In this paper, we develop a framework to obtain graph abstractions for decision-making by an agent where the abstractions emerge as a function of the agent's limited computational resources. We discuss the connection of the proposed approach with information-theoretic signal compression, and formulate a novel optimization problem to obtain tree-based abstractions as a function of the agent's computational resources. The structural properties of the new problem are discussed in detail, and two algorithmic approaches are proposed to obtain solutions to this optimization problem. We discuss the quality of, and prove relationships between, solutions obtained by the two proposed algorithms. The framework is demonstrated to generate a hierarchy of abstractions for a non-trivial environment.

Neural architecture search methods are able to find high performance deep learning architectures with minimal effort from an expert. However, current systems focus on specific use-cases (e.g. convolutional image classifiers and recurrent language models), making them unsuitable for general use-cases that an expert might wish to write. Hyperparameter optimization systems are general-purpose but lack the constructs needed for easy application to architecture search. In this work, we propose a formal language for encoding search spaces over general computational graphs. The language constructs allow us to write modular, composable, and reusable search space encodings and to reason about search space design. We use our language to encode search spaces from the architecture search literature. The language allows us to decouple the implementations of the search space and the search algorithm, allowing us to expose search spaces to search algorithms through a consistent interface. Our experiments show the ease with which we can experiment with different combinations of search spaces and search algorithms without having to implement each combination from scratch. We release an implementation of our language with this paper.

Combinatorial optimization is the field devoted to the study and practice of algorithms that solve NP-hard problems. As Machine Learning (ML) and deep learning have popularized, several research groups have started to use ML to solve combinatorial optimization problems, such as the well-known Travelling Salesman Problem (TSP). Based on deep (reinforcement) learning, new models and architecture for the TSP have been successively developed and have gained increasing performances. At the time of writing, state-of-the-art models provide solutions to TSP instances of 100 cities that are roughly 1.33% away from optimal solutions. However, despite these apparently positive results, the performances remain far from those that can be achieved using a specialized search procedure. In this paper, we address the limitations of ML approaches for solving the TSP and investigate two fundamental questions: (1) how can we measure the level of accuracy of the pure ML component of such methods; and (2) what is the impact of a search procedure plugged inside a ML model on the performances? To answer these questions, we propose a new metric, ratio of optimal decisions (ROD), based on a fair comparison with a parametrized oracle, mimicking a ML model with a controlled accuracy. All the experiments are carried out on four state-of-the-art ML approaches dedicated to solve the TSP. Finally, we made ROD open-source in order to ease future research in the field.