arXiv subjects

Paul Christiano

Publications and source records attributed to Paul Christiano.

27 records · Page 2Linked to original sources

arXiv2016

A Connection between Generative Adversarial Networks, Inverse Reinforcement Learning, and Energy-Based Models

Generative adversarial networks (GANs) are a recently proposed class of generative models in which a generator is trained to optimize a cost function that is being simultaneously learned by a discriminator. While the idea of learning cost functions is relatively new to the field of generative modeling, learning costs has long been studied in control and reinforcement learning (RL) domains, typically for imitation learning from demonstrations. In these fields, learning cost function underlying observed behavior is known as inverse reinforcement learning (IRL) or inverse optimal control. While at first the connection between cost learning in RL and cost learning in generative modeling may appear to be a superficial one, we show in this paper that certain IRL methods are in fact mathematically equivalent to GANs. In particular, we demonstrate an equivalence between a sample-based algorithm for maximum entropy IRL and a GAN in which the generator's density can be evaluated and is provided as an additional input to the discriminator. Interestingly, maximum entropy IRL is a special case of an energy-based model. We discuss the interpretation of GANs as an algorithm for training energy-based models, and relate this interpretation to other recent work that seeks to connect GANs and EBMs. By formally highlighting the connection between GANs, IRL, and EBMs, we hope that researchers in all three communities can better identify and apply transferable ideas from one domain to another, particularly for developing more stable and scalable algorithms: a major challenge in all three domains.

cs.LG↗

arXiv2016

Transfer from Simulation to Real World through Learning Deep Inverse Dynamics Model

Developing control policies in simulation is often more practical and safer than directly running experiments in the real world. This applies to policies obtained from planning and optimization, and even more so to policies obtained from reinforcement learning, which is often very data demanding. However, a policy that succeeds in simulation often doesn't work when deployed on a real robot. Nevertheless, often the overall gist of what the policy does in simulation remains valid in the real world. In this paper we investigate such settings, where the sequence of states traversed in simulation remains reasonable for the real world, even if the details of the controls are not, as could be the case when the key differences lie in detailed friction, contact, mass and geometry properties. During execution, at each time step our approach computes what the simulation-based control policy would do, but then, rather than executing these controls on the real robot, our approach computes what the simulation expects the resulting next state(s) will be, and then relies on a learned deep inverse dynamics model to decide which real-world action is most suitable to achieve those next states. Deep models are only as good as their training data, and we also propose an approach for data collection to (incrementally) learn the deep inverse dynamics model. Our experiments shows our approach compares favorably with various baselines that have been developed for dealing with simulation to real world model discrepancy, including output error control and Gaussian dynamics adaptation.

cs.RO↗

arXiv2016

Concrete Problems in AI Safety

Rapid progress in machine learning and artificial intelligence (AI) has brought increasing attention to the potential impacts of AI technologies on society. In this paper we discuss one such potential impact: the problem of accidents in machine learning systems, defined as unintended and harmful behavior that may emerge from poor design of real-world AI systems. We present a list of five practical research problems related to accident risk, categorized according to whether the problem originates from having the wrong objective function ("avoiding side effects" and "avoiding reward hacking"), an objective function that is too expensive to evaluate frequently ("scalable supervision"), or undesirable behavior during the learning process ("safe exploration" and "distributional shift"). We review previous work in these areas as well as suggesting research directions with a focus on relevance to cutting-edge AI systems. Finally, we consider the high-level question of how to think most productively about the safety of forward-looking applications of AI.

cs.AI↗

arXiv2016

Theano: A Python framework for fast computation of mathematical expressions

Theano is a Python library that allows to define, optimize, and evaluate mathematical expressions involving multi-dimensional arrays efficiently. Since its introduction, it has been one of the most used CPU and GPU mathematical compilers - especially in the machine learning community - and has shown steady performance improvements. Theano is being actively and continuously developed since 2008, multiple frameworks have been built on top of it and it has been used to produce many state-of-the-art machine learning models. The present article is structured as follows. Section I provides an overview of the Theano software and its community. Section II presents the principal features of Theano and how to use them, and compares them with other similar projects. Section III focuses on recently-introduced functionalities and improvements. Section IV compares the performance of Theano against Torch7 and TensorFlow on several machine learning models. Section V discusses current limitations of Theano and potential ways of improving it.

cs.SC↗

arXiv2016

Collaborative prediction with expert advice

Many practical learning systems aggregate data across many users, while learning theory traditionally considers a single learner who trusts all of their observations. A case in point is the foundational learning problem of prediction with expert advice. To date, there has been no theoretical study of the general collaborative version of prediction with expert advice, in which many users face a similar problem and would like to share their experiences in order to learn faster. A key issue in this collaborative framework is robustness: generally algorithms that aggregate data are vulnerable to manipulation by even a small number of dishonest users. We exhibit the first robust collaborative algorithm for prediction with expert advice. When all users are honest and have similar tastes our algorithm matches the performance of pooling data and using a traditional algorithm. But our algorithm also guarantees that adding users never significantly degrades performance, even if the additional users behave adversarially. We achieve strong guarantees even when the overwhelming majority of users behave adversarially. As a special case, our algorithm is extremely robust to variation amongst the users.

cs.LG↗

arXiv2014

Provably Manipulation-Resistant Reputation Systems

We consider a community of users who must make periodic decisions about whether to interact with one another. We propose a protocol which allows honest users to reliably interact with each other, while limiting the damage done by each malicious or incompetent user. The worst-case cost per user is sublinear in the average number of interactions per user and is independent of the number of users. Our guarantee holds simultaneously for every group of honest users. For example, multiple groups of users with incompatible tastes or preferences can coexist. As a motivating example, we consider a game where players have periodic opportunities to do one another favors but minimal ability to determine when a favor was done. In this setting, our protocol achieves nearly optimal collective welfare while remaining resistant to exploitation. Our results also apply to a collaborative filtering setting where users must make periodic decisions about whether to interact with resources such as movies or restaurants. In this setting, we guarantee that any set of honest users achieves a payoff nearly as good as if they had identified the optimal set of items in advance and then chosen to interact only with resources from that set.

cs.GT↗

arXiv2014

Online Local Learning via Semidefinite Programming

In many online learning problems we are interested in predicting local information about some universe of items. For example, we may want to know whether two items are in the same cluster rather than computing an assignment of items to clusters; we may want to know which of two teams will win a game rather than computing a ranking of teams. Although finding the optimal clustering or ranking is typically intractable, it may be possible to predict the relationships between items as well as if you could solve the global optimization problem exactly. Formally, we consider an online learning problem in which a learner repeatedly guesses a pair of labels (l(x), l(y)) and receives an adversarial payoff depending on those labels. The learner's goal is to receive a payoff nearly as good as the best fixed labeling of the items. We show that a simple algorithm based on semidefinite programming can obtain asymptotically optimal regret in the case where the number of possible labels is O(1), resolving an open problem posed by Hazan, Kale, and Shalev-Schwartz. Our main technical contribution is a novel use and analysis of the log determinant regularizer, exploiting the observation that log det(A + I) upper bounds the entropy of any distribution with covariance matrix A.

cs.LG↗

arXiv2012

Quantum Money from Hidden Subspaces

Forty years ago, Wiesner pointed out that quantum mechanics raises the striking possibility of money that cannot be counterfeited according to the laws of physics. We propose the first quantum money scheme that is (1) public-key, meaning that anyone can verify a banknote as genuine, not only the bank that printed it, and (2) cryptographically secure, under a "classical" hardness assumption that has nothing to do with quantum money. Our scheme is based on hidden subspaces, encoded as the zero-sets of random multivariate polynomials. A main technical advance is to show that the "black-box" version of our scheme, where the polynomials are replaced by classical oracles, is unconditionally secure. Previously, such a result had only been known relative to a quantum oracle (and even there, the proof was never published). Even in Wiesner's original setting -- quantum money that can only be verified by the bank -- we are able to use our techniques to patch a major security hole in Wiesner's scheme. We give the first private-key quantum money scheme that allows unlimited verifications and that remains unconditionally secure, even if the counterfeiter can interact adaptively with the bank. Our money scheme is simpler than previous public-key quantum money schemes, including a knot-based scheme of Farhi et al. The verifier needs to perform only two tests, one in the standard basis and one in the Hadamard basis -- matching the original intuition for quantum money, based on the existence of complementary observables. Our security proofs use a new variant of Ambainis's quantum adversary method, and several other tools that might be of independent interest.

quant-ph↗

arXiv2010

Electrical Flows, Laplacian Systems, and Faster Approximation of Maximum Flow in Undirected Graphs

We introduce a new approach to computing an approximately maximum s-t flow in a capacitated, undirected graph. This flow is computed by solving a sequence of electrical flow problems. Each electrical flow is given by the solution of a system of linear equations in a Laplacian matrix, and thus may be approximately computed in nearly-linear time. Using this approach, we develop the fastest known algorithm for computing approximately maximum s-t flows. For a graph having n vertices and m edges, our algorithm computes a (1-ε)-approximately maximum s-t flow in time \tilde{O}(mn^{1/3} ε^{-11/3}). A dual version of our approach computes a (1+ε)-approximately minimum s-t cut in time \tilde{O}(m+n^{4/3}\eps^{-8/3}), which is the fastest known algorithm for this problem as well. Previously, the best dependence on m and n was achieved by the algorithm of Goldberg and Rao (J. ACM 1998), which can be used to compute approximately maximum s-t flows in time \tilde{O}(m\sqrt{n}ε^{-1}), and approximately minimum s-t cuts in time \tilde{O}(m+n^{3/2}ε^{-3}).

cs.DS↗