arXiv subjects

Christoph Dann

Publications and source records attributed to Christoph Dann.

35 records · Page 2Linked to original sources

arXiv2022

Same Cause; Different Effects in the Brain

To study information processing in the brain, neuroscientists manipulate experimental stimuli while recording participant brain activity. They can then use encoding models to find out which brain "zone" (e.g. which region of interest, volume pixel or electrophysiology sensor) is predicted from the stimulus properties. Given the assumptions underlying this setup, when stimulus properties are predictive of the activity in a zone, these properties are understood to cause activity in that zone. In recent years, researchers have used neural networks to construct representations that capture the diverse properties of complex stimuli, such as natural language or natural images. Encoding models built using these high-dimensional representations are often able to significantly predict the activity in large swathes of cortex, suggesting that the activity in all these brain zones is caused by stimulus properties captured in the representation. It is then natural to ask: "Is the activity in these different brain zones caused by the stimulus properties in the same way?" In neuroscientific terms, this corresponds to asking if these different zones process the stimulus properties in the same way. Here, we propose a new framework that enables researchers to ask if the properties of a stimulus affect two brain zones in the same way. We use simulated data and two real fMRI datasets with complex naturalistic stimuli to show that our framework enables us to make such inferences. Our inferences are strikingly consistent between the two datasets, indicating that the proposed framework is a promising new tool for neuroscientists to understand how information is processed in the brain.

q-bio.NC↗

arXiv2021

Beyond Value-Function Gaps: Improved Instance-Dependent Regret Bounds for Episodic Reinforcement Learning

We provide improved gap-dependent regret bounds for reinforcement learning in finite episodic Markov decision processes. Compared to prior work, our bounds depend on alternative definitions of gaps. These definitions are based on the insight that, in order to achieve a favorable regret, an algorithm does not need to learn how to behave optimally in states that are not reached by an optimal policy. We prove tighter upper regret bounds for optimistic algorithms and accompany them with new information-theoretic lower bounds for a large class of MDPs. Our results show that optimistic algorithms can not achieve the information-theoretic lower bounds even in deterministic MDPs unless there is a unique optimal policy.

cs.LG↗

arXiv2021

Agnostic Reinforcement Learning with Low-Rank MDPs and Rich Observations

There have been many recent advances on provably efficient Reinforcement Learning (RL) in problems with rich observation spaces. However, all these works share a strong realizability assumption about the optimal value function of the true MDP. Such realizability assumptions are often too strong to hold in practice. In this work, we consider the more realistic setting of agnostic RL with rich observation spaces and a fixed class of policies $Π$ that may not contain any near-optimal policy. We provide an algorithm for this setting whose error is bounded in terms of the rank $d$ of the underlying MDP. Specifically, our algorithm enjoys a sample complexity bound of $\widetilde{O}\left((H^{4d} K^{3d} \log |Π|)/ε^2\right)$ where $H$ is the length of episodes, $K$ is the number of actions and $ε>0$ is the desired sub-optimality. We also provide a nearly matching lower bound for this agnostic setting that shows that the exponential dependence on rank is unavoidable, without further assumptions.

cs.LG↗

arXiv2021

Neural Active Learning with Performance Guarantees

We investigate the problem of active learning in the streaming setting in non-parametric regimes, where the labels are stochastically generated from a class of functions on which we make no assumptions whatsoever. We rely on recently proposed Neural Tangent Kernel (NTK) approximation tools to construct a suitable neural embedding that determines the feature space the algorithm operates on and the learned model computed atop. Since the shape of the label requesting threshold is tightly related to the complexity of the function to be learned, which is a-priori unknown, we also derive a version of the algorithm which is agnostic to any prior knowledge. This algorithm relies on a regret balancing scheme to solve the resulting online model selection problem, and is computationally efficient. We prove joint guarantees on the cumulative regret and number of requested labels which depend on the complexity of the labeling function at hand. In the linear case, these guarantees recover known minimax results of the generalization error as a function of the label complexity in a standard statistical learning setting.

cs.LG↗

arXiv2020

Regret Bound Balancing and Elimination for Model Selection in Bandits and RL

We propose a simple model selection approach for algorithms in stochastic bandit and reinforcement learning problems. As opposed to prior work that (implicitly) assumes knowledge of the optimal regret, we only require that each base algorithm comes with a candidate regret bound that may or may not hold during all rounds. In each round, our approach plays a base algorithm to keep the candidate regret bounds of all remaining base algorithms balanced, and eliminates algorithms that violate their candidate bound. We prove that the total regret of this approach is bounded by the best valid candidate regret bound times a multiplicative factor. This factor is reasonably small in several applications, including linear bandits and MDPs with nested function classes, linear bandits with unknown misspecification, and LinUCB applied to linear bandits with different confidence parameters. We further show that, under a suitable gap-assumption, this factor only scales with the number of base algorithms and not their complexity when the number of rounds is large enough. Finally, unlike recent efforts in model selection for linear stochastic bandits, our approach is versatile enough to also cover cases where the context information is generated by an adversarial environment, rather than a stochastic one.

cs.LG↗

arXiv2020

Reinforcement Learning with Feedback Graphs

We study episodic reinforcement learning in Markov decision processes when the agent receives additional feedback per step in the form of several transition observations. Such additional observations are available in a range of tasks through extended sensors or prior knowledge about the environment (e.g., when certain actions yield similar outcome). We formalize this setting using a feedback graph over state-action pairs and show that model-based algorithms can leverage the additional feedback for more sample-efficient learning. We give a regret bound that, ignoring logarithmic factors and lower-order terms, depends only on the size of the maximum acyclic subgraph of the feedback graph, in contrast with a polynomial dependency on the number of states and actions in the absence of a feedback graph. Finally, we highlight challenges when leveraging a small dominating set of the feedback graph as compared to the bandit setting and propose a new algorithm that can use knowledge of such a dominating set for more sample-efficient learning of a near-optimal policy.

cs.LG↗

arXiv2020

Being Optimistic to Be Conservative: Quickly Learning a CVaR Policy

While maximizing expected return is the goal in most reinforcement learning approaches, risk-sensitive objectives such as conditional value at risk (CVaR) are more suitable for many high-stakes applications. However, relatively little is known about how to explore to quickly learn policies with good CVaR. In this paper, we present the first algorithm for sample-efficient learning of CVaR-optimal policies in Markov decision processes based on the optimism in the face of uncertainty principle. This method relies on a novel optimistic version of the distributional Bellman operator that moves probability mass from the lower to the upper tail of the return distribution. We prove asymptotic convergence and optimism of this operator for the tabular policy evaluation case. We further demonstrate that our algorithm finds CVaR-optimal policies substantially faster than existing baselines in several simulated environments with discrete and continuous state spaces.

cs.LG↗

arXiv2019

Policy Certificates: Towards Accountable Reinforcement Learning

The performance of a reinforcement learning algorithm can vary drastically during learning because of exploration. Existing algorithms provide little information about the quality of their current policy before executing it, and thus have limited use in high-stakes applications like healthcare. We address this lack of accountability by proposing that algorithms output policy certificates. These certificates bound the sub-optimality and return of the policy in the next episode, allowing humans to intervene when the certified quality is not satisfactory. We further introduce two new algorithms with certificates and present a new framework for theoretical analysis that guarantees the quality of their policies and certificates. For tabular MDPs, we show that computing certificates can even improve the sample-efficiency of optimism-based exploration. As a result, one of our algorithms is the first to achieve minimax-optimal PAC bounds up to lower-order terms, and this algorithm also matches (and in some settings slightly improves upon) existing minimax regret bounds.

cs.LG↗

arXiv2019

On Oracle-Efficient PAC RL with Rich Observations

We study the computational tractability of PAC reinforcement learning with rich observations. We present new provably sample-efficient algorithms for environments with deterministic hidden state dynamics and stochastic rich observations. These methods operate in an oracle model of computation -- accessing policy and value function classes exclusively through standard optimization primitives -- and therefore represent computationally efficient alternatives to prior algorithms that require enumeration. With stochastic hidden state dynamics, we prove that the only known sample-efficient algorithm, OLIVE, cannot be implemented in the oracle model. We also present several examples that illustrate fundamental challenges of tractable PAC reinforcement learning in such general settings.

cs.LG↗

arXiv2018

Unifying PAC and Regret: Uniform PAC Bounds for Episodic Reinforcement Learning

Statistical performance bounds for reinforcement learning (RL) algorithms can be critical for high-stakes applications like healthcare. This paper introduces a new framework for theoretically measuring the performance of such algorithms called Uniform-PAC, which is a strengthening of the classical Probably Approximately Correct (PAC) framework. In contrast to the PAC framework, the uniform version may be used to derive high probability regret guarantees and so forms a bridge between the two setups that has been missing in the literature. We demonstrate the benefits of the new framework for finite-state episodic MDPs with a new algorithm that is Uniform-PAC and simultaneously achieves optimal regret and PAC guarantees except for a factor of the horizon.

cs.LG↗

arXiv2017

Decoupling Learning Rules from Representations

In the artificial intelligence field, learning often corresponds to changing the parameters of a parameterized function. A learning rule is an algorithm or mathematical expression that specifies precisely how the parameters should be changed. When creating an artificial intelligence system, we must make two decisions: what representation should be used (i.e., what parameterized function should be used) and what learning rule should be used to search through the resulting set of representable functions. Using most learning rules, these two decisions are coupled in a subtle (and often unintentional) way. That is, using the same learning rule with two different representations that can represent the same sets of functions can result in two different outcomes. After arguing that this coupling is undesirable, particularly when using artificial neural networks, we present a method for partially decoupling these two decisions for a broad class of learning rules that span unsupervised learning, reinforcement learning, and supervised learning.

cs.AI↗

arXiv2017

Sample Efficient Policy Search for Optimal Stopping Domains

Optimal stopping problems consider the question of deciding when to stop an observation-generating process in order to maximize a return. We examine the problem of simultaneously learning and planning in such domains, when data is collected directly from the environment. We propose GFSE, a simple and flexible model-free policy search method that reuses data for sample efficiency by leveraging problem structure. We bound the sample complexity of our approach to guarantee uniform convergence of policy value estimates, tightening existing PAC bounds to achieve logarithmic dependence on horizon length for our setting. We also examine the benefit of our method against prevalent model-based and model-free approaches on 3 domains taken from diverse fields.

cs.AI↗

arXiv2016

Memory Lens: How Much Memory Does an Agent Use?

We propose a new method to study the internal memory used by reinforcement learning policies. We estimate the amount of relevant past information by estimating mutual information between behavior histories and the current action of an agent. We perform this estimation in the passive setting, that is, we do not intervene but merely observe the natural behavior of the agent. Moreover, we provide a theoretical justification for our approach by showing that it yields an implementation-independent lower bound on the minimal memory capacity of any agent that implement the observed policy. We demonstrate our approach by estimating the use of memory of DQN policies on concatenated Atari frames, demonstrating sharply different use of memory across 49 games. The study of memory as information that flows from the past to the current action opens avenues to understand and improve successful reinforcement learning algorithms.

cs.AI↗

arXiv2016

Sample Complexity of Episodic Fixed-Horizon Reinforcement Learning

Recently, there has been significant progress in understanding reinforcement learning in discounted infinite-horizon Markov decision processes (MDPs) by deriving tight sample complexity bounds. However, in many real-world applications, an interactive learning agent operates for a fixed or bounded period of time, for example tutoring students for exams or handling customer service requests. Such scenarios can often be better treated as episodic fixed-horizon MDPs, for which only looser bounds on the sample complexity exist. A natural notion of sample complexity in this setting is the number of episodes required to guarantee a certain performance with high probability (PAC guarantee). In this paper, we derive an upper PAC bound $\tilde O(\frac{|\mathcal S|^2 |\mathcal A| H^2}{ε^2} \ln\frac 1 δ)$ and a lower PAC bound $\tilde Ω(\frac{|\mathcal S| |\mathcal A| H^2}{ε^2} \ln \frac 1 {δ+ c})$ that match up to log-terms and an additional linear dependency on the number of states $|\mathcal S|$. The lower bound is the first of its kind for this setting. Our upper bound leverages Bernstein's inequality to improve on previous bounds for episodic finite-horizon MDPs which have a time-horizon dependency of at least $H^3$.

stat.ML↗

arXiv2015

The Human Kernel

Bayesian nonparametric models, such as Gaussian processes, provide a compelling framework for automatic statistical modelling: these models have a high degree of flexibility, and automatically calibrated complexity. However, automating human expertise remains elusive; for example, Gaussian processes with standard kernels struggle on function extrapolation problems that are trivial for human learners. In this paper, we create function extrapolation problems and acquire human responses, and then design a kernel learning framework to reverse engineer the inductive biases of human learners across a set of behavioral experiments. We use the learned kernels to gain psychological insights and to extrapolate in human-like ways that go beyond traditional stationary and polynomial kernels. Finally, we investigate Occam's razor in human and Gaussian process based function learning.

cs.LG↗

arXiv2015

Thoughts on Massively Scalable Gaussian Processes

We introduce a framework and early results for massively scalable Gaussian processes (MSGP), significantly extending the KISS-GP approach of Wilson and Nickisch (2015). The MSGP framework enables the use of Gaussian processes (GPs) on billions of datapoints, without requiring distributed inference, or severe assumptions. In particular, MSGP reduces the standard $O(n^3)$ complexity of GP learning and inference to $O(n)$, and the standard $O(n^2)$ complexity per test point prediction to $O(1)$. MSGP involves 1) decomposing covariance matrices as Kronecker products of Toeplitz matrices approximated by circulant matrices. This multi-level circulant approximation allows one to unify the orthogonal computational benefits of fast Kronecker and Toeplitz approaches, and is significantly faster than either approach in isolation; 2) local kernel interpolation and inducing points to allow for arbitrarily located data inputs, and $O(1)$ test time predictions; 3) exploiting block-Toeplitz Toeplitz-block structure (BTTB), which enables fast inference and learning when multidimensional Kronecker structure is not present; and 4) projections of the input space to flexibly model correlated inputs and high dimensional data. The ability to handle many ($m \approx n$) inducing points allows for near-exact accuracy and large scale kernel learning.

cs.LG↗

arXiv2015

Bayesian Time-of-Flight for Realtime Shape, Illumination and Albedo

We propose a computational model for shape, illumination and albedo inference in a pulsed time-of-flight (TOF) camera. In contrast to TOF cameras based on phase modulation, our camera enables general exposure profiles. This results in added flexibility and requires novel computational approaches. To address this challenge we propose a generative probabilistic model that accurately relates latent imaging conditions to observed camera responses. While principled, realtime inference in the model turns out to be infeasible, and we propose to employ efficient non-parametric regression trees to approximate the model outputs. As a result we are able to provide, for each pixel, at video frame rate, estimates and uncertainty for depth, effective albedo, and ambient light intensity. These results we present are state-of-the-art in depth imaging. The flexibility of our approach allows us to easily enrich our generative model. We demonstrate that by extending the original single-path model to a two-path model, capable of describing some multipath effects. The new model is seamlessly integrated in the system at no additional computational cost. Our work also addresses the important question of optimal exposure design in pulsed TOF systems. Finally, for benchmark purposes and to obtain realistic empirical priors of multipath and insights into this phenomena, we propose a physically accurate simulation of multipath phenomena.

cs.CV↗