Diana Borsa

Shantanu Thakoor, Mark Rowland, Diana Borsa et al.

We introduce a method for policy improvement that interpolates between the greedy approach of value-based reinforcement learning (RL) and the full planning approach typical of model-based RL. The new method builds on the concept of a geometric horizon model (GHM, also known as a gamma-model), which models the discounted state-visitation distribution of a given policy. We show that we can evaluate any non-Markov policy that switches between a set of base Markov policies with fixed probability by a careful composition of the base policy GHMs, without any additional learning. We can then apply generalised policy improvement (GPI) to collections of such non-Markov policies to obtain a new Markov policy that will in general outperform its precursors. We provide a thorough theoretical analysis of this approach, develop applications to transfer and standard RL, and empirically demonstrate its effectiveness over standard GPI on a challenging deep RL continuous control task. We also provide an analysis of GHM training methods, proving a novel convergence result regarding previously proposed methods and showing how to train these models stably in deep RL settings.

Ted Moskovitz, Samo Hromadka, Ahmed Touati et al.

A common setting in multitask reinforcement learning (RL) demands that an agent rapidly adapt to various stationary reward functions randomly sampled from a fixed distribution. In such situations, the successor representation (SR) is a popular framework which supports rapid policy evaluation by decoupling a policy's expected discounted, cumulative state occupancies from a specific reward function. However, in the natural world, sequential tasks are rarely independent, and instead reflect shifting priorities based on the availability and subjective perception of rewarding stimuli. Reflecting this disjunction, in this paper we study the phenomenon of diminishing marginal utility and introduce a novel state representation, the $λ$ representation ($λ$R) which, surprisingly, is required for policy evaluation in this setting and which generalizes the SR as well as several other state representations from the literature. We establish the $λ$R's formal properties and examine its normative advantages in the context of machine learning, as well as its usefulness for studying natural behaviors, particularly foraging.

Bernardo Ávila Pires, Mark Rowland, Diana Borsa et al.

We introduce distributional dynamic programming (DP) methods for optimizing statistical functionals of the return distribution, with standard reinforcement learning as a special case. Previous distributional DP methods could optimize the same class of expected utilities as classic DP. To go beyond, we combine distributional DP with stock augmentation, a technique previously introduced for classic DP in the context of risk-sensitive RL, where the MDP state is augmented with a statistic of the rewards obtained since the first time step. We find that a number of recently studied problems can be formulated as stock-augmented return distribution optimization, and we show that we can use distributional DP to solve them. We analyze distributional value and policy iteration, with bounds and a study of what objectives these distributional DP methods can or cannot optimize. We describe a number of applications outlining how to use distributional DP to solve different stock-augmented return distribution optimization problems, for example maximizing conditional value-at-risk, and homeostatic regulation. To highlight the practical potential of stock-augmented return distribution optimization and distributional DP, we introduce an agent that combines DQN and the core ideas of distributional DP, and empirically evaluate it for solving instances of the applications discussed.

David Pfau, Ian Davies, Diana Borsa et al.

We introduce Wasserstein Policy Optimization (WPO), an actor-critic algorithm for reinforcement learning in continuous action spaces. WPO can be derived as an approximation to Wasserstein gradient flow over the space of all policies projected into a finite-dimensional parameter space (e.g., the weights of a neural network), leading to a simple and completely general closed-form update. The resulting algorithm combines many properties of deterministic and classic policy gradient methods. Like deterministic policy gradients, it exploits knowledge of the gradient of the action-value function with respect to the action. Like classic policy gradients, it can be applied to stochastic policies with arbitrary distributions over actions -- without using the reparameterization trick. We show results on the DeepMind Control Suite and a magnetic confinement fusion task which compare favorably with state-of-the-art continuous control methods.

Khimya Khetarpal, Zhaohan Daniel Guo, Bernardo Avila Pires et al.

Learning a good representation is a crucial challenge for Reinforcement Learning (RL) agents. Self-predictive learning provides means to jointly learn a latent representation and dynamics model by bootstrapping from future latent representations (BYOL). Recent work has developed theoretical insights into these algorithms by studying a continuous-time ODE model for self-predictive representation learning under the simplifying assumption that the algorithm depends on a fixed policy (BYOL-$Π$); this assumption is at odds with practical instantiations of such algorithms, which explicitly condition their predictions on future actions. In this work, we take a step towards bridging the gap between theory and practice by analyzing an action-conditional self-predictive objective (BYOL-AC) using the ODE framework, characterizing its convergence properties and highlighting important distinctions between the limiting solutions of the BYOL-$Π$ and BYOL-AC dynamics. We show how the two representations are related by a variance equation. This connection leads to a novel variance-like action-conditional objective (BYOL-VAR) and its corresponding ODE. We unify the study of all three objectives through two complementary lenses; a model-based perspective, where each objective is shown to be equivalent to a low-rank approximation of certain dynamics, and a model-free perspective, which establishes relationships between the objectives and their respective value, Q-value, and advantage function. Our empirical investigations, encompassing both linear function approximation and Deep RL environments, demonstrates that BYOL-AC is better overall in a variety of different settings.

Veronica Chelu, Diana Borsa, Doina Precup et al.

Efficient credit assignment is essential for reinforcement learning algorithms in both prediction and control settings. We describe a unified view on temporal-difference algorithms for selective credit assignment. These selective algorithms apply weightings to quantify the contribution of learning updates. We present insights into applying weightings to value-based learning and planning algorithms, and describe their role in mediating the backward credit distribution in prediction and control. Within this space, we identify some existing online learning algorithms that can assign credit selectively as special cases, as well as add new algorithms that assign credit backward in time counterfactually, allowing credit to be assigned off-trajectory and off-policy.

Angelos Filos, Eszter Vértes, Zita Marinho et al.

Using a model of the environment and a value function, an agent can construct many estimates of a state's value, by unrolling the model for different lengths and bootstrapping with its value function. Our key insight is that one can treat this set of value estimates as a type of ensemble, which we call an \emph{implicit value ensemble} (IVE). Consequently, the discrepancy between these estimates can be used as a proxy for the agent's epistemic uncertainty; we term this signal \emph{model-value inconsistency} or \emph{self-inconsistency} for short. Unlike prior work which estimates uncertainty by training an ensemble of many models and/or value functions, this approach requires only the single model and value function which are already being learned in most model-based reinforcement learning algorithms. We provide empirical evidence in both tabular and function approximation settings from pixels that self-inconsistency is useful (i) as a signal for exploration, (ii) for acting safely under distribution shifts, and (iii) for robustifying value-based planning with a learned model.

Miruna Pîslar, David Szepesvari, Georg Ostrovski et al.

Exploration remains a central challenge for reinforcement learning (RL). Virtually all existing methods share the feature of a monolithic behaviour policy that changes only gradually (at best). In contrast, the exploratory behaviours of animals and humans exhibit a rich diversity, namely including forms of switching between modes. This paper presents an initial study of mode-switching, non-monolithic exploration for RL. We investigate different modes to switch between, at what timescales it makes sense to switch, and what signals make for good switching triggers. We also propose practical algorithmic components that make the switching mechanism adaptive and robust, which enables flexibility without an accompanying hyper-parameter-tuning burden. Finally, we report a promising and detailed analysis on Atari, using two-mode exploration and switching at sub-episodic time-scales.

André Barreto, Diana Borsa, Shaobo Hou et al.

The ability to combine known skills to create new ones may be crucial in the solution of complex reinforcement learning problems that unfold over extended periods. We argue that a robust way of combining skills is to define and manipulate them in the space of pseudo-rewards (or "cumulants"). Based on this premise, we propose a framework for combining skills using the formalism of options. We show that every deterministic option can be unambiguously represented as a cumulant defined in an extended domain. Building on this insight and on previous results on transfer learning, we show how to approximate options whose cumulants are linear combinations of the cumulants of known options. This means that, once we have learned options associated with a set of cumulants, we can instantaneously synthesise options induced by any linear combination of them, without any learning involved. We describe how this framework provides a hierarchical interface to the environment whose abstract actions correspond to combinations of basic skills. We demonstrate the practical benefits of our approach in a resource management problem and a navigation task involving a quadrupedal simulated robot.

Tom Schaul, Georg Ostrovski, Iurii Kemaev et al.

Scaling issues are mundane yet irritating for practitioners of reinforcement learning. Error scales vary across domains, tasks, and stages of learning; sometimes by many orders of magnitude. This can be detrimental to learning speed and stability, create interference between learning tasks, and necessitate substantial tuning. We revisit this topic for agents based on temporal-difference learning, sketch out some desiderata and investigate scenarios where simple fixes fall short. The mechanism we propose requires neither tuning, clipping, nor adaptation. We validate its effectiveness and robustness on the suite of Atari games. Our scaling method turns out to be particularly helpful at mitigating interference, when training a shared neural network on multiple targets that differ in reward scale or discounting.

Hado van Hasselt, Sephora Madjiheurem, Matteo Hessel et al.

The question of how to determine which states and actions are responsible for a certain outcome is known as the credit assignment problem and remains a central research question in reinforcement learning and artificial intelligence. Eligibility traces enable efficient credit assignment to the recent sequence of states and actions experienced by the agent, but not to counterfactual sequences that could also have led to the current state. In this work, we introduce expected eligibility traces. Expected traces allow, with a single update, to update states and actions that could have preceded the current state, even if they did not do so on this occasion. We discuss when expected traces provide benefits over classic (instantaneous) traces in temporal-difference learning, and show that sometimes substantial improvements can be attained. We provide a way to smoothly interpolate between instantaneous and expected traces by a mechanism similar to bootstrapping, which ensures that the resulting algorithm is a strict generalisation of TD($λ$). Finally, we discuss possible extensions and connections to related ideas, such as successor features.

Tom Schaul, Diana Borsa, David Ding et al.

Determining what experience to generate to best facilitate learning (i.e. exploration) is one of the distinguishing features and open challenges in reinforcement learning. The advent of distributed agents that interact with parallel instances of the environment has enabled larger scales and greater flexibility, but has not removed the need to tune exploration to the task, because the ideal data for the learning algorithm necessarily depends on its process of learning. We propose to dynamically adapt the data generation by using a non-stationary multi-armed bandit to optimize a proxy of the learning progress. The data distribution is controlled by modulating multiple parameters of the policy (such as stochasticity, consistency or optimism) without significant overhead. The adaptation speed of the bandit can be increased by exploiting the factored modulation structure. We demonstrate on a suite of Atari 2600 games how this unified approach produces results comparable to per-task tuning at a fraction of the cost.

Mark Rowland, Anna Harutyunyan, Hado van Hasselt et al.

The principal contribution of this paper is a conceptual framework for off-policy reinforcement learning, based on conditional expectations of importance sampling ratios. This framework yields new perspectives and understanding of existing off-policy algorithms, and reveals a broad space of unexplored algorithms. We theoretically analyse this space, and concretely investigate several algorithms that arise from this framework.

Hado van Hasselt, John Quan, Matteo Hessel et al.

We consider a general class of non-linear Bellman equations. These open up a design space of algorithms that have interesting properties, which has two potential advantages. First, we can perhaps better model natural phenomena. For instance, hyperbolic discounting has been proposed as a mathematical model that matches human and animal data well, and can therefore be used to explain preference orderings. We present a different mathematical model that matches the same data, but that makes very different predictions under other circumstances. Second, the larger design space can perhaps lead to algorithms that perform better, similar to how discount factors are often used in practice even when the true objective is undiscounted. We show that many of the resulting Bellman operators still converge to a fixed point, and therefore that the resulting algorithms are reasonable and inherit many beneficial properties of their linear counterparts.

Tom Schaul, Diana Borsa, Joseph Modayil et al.

Rather than proposing a new method, this paper investigates an issue present in existing learning algorithms. We study the learning dynamics of reinforcement learning (RL), specifically a characteristic coupling between learning and data generation that arises because RL agents control their future data distribution. In the presence of function approximation, this coupling can lead to a problematic type of 'ray interference', characterized by learning dynamics that sequentially traverse a number of performance plateaus, effectively constraining the agent to learn one thing at a time even when learning in parallel is better. We establish the conditions under which ray interference occurs, show its relation to saddle points and obtain the exact learning dynamics in a restricted setting. We characterize a number of its properties and discuss possible remedies.

Anna Harutyunyan, Will Dabney, Diana Borsa et al.

In this work, we consider the problem of autonomously discovering behavioral abstractions, or options, for reinforcement learning agents. We propose an algorithm that focuses on the termination condition, as opposed to -- as is common -- the policy. The termination condition is usually trained to optimize a control objective: an option ought to terminate if another has better value. We offer a different, information-theoretic perspective, and propose that terminations should focus instead on the compressibility of the option's encoding -- arguably a key reason for using abstractions. To achieve this algorithmically, we leverage the classical options framework, and learn the option transition model as a "critic" for the termination condition. Using this model, we derive gradients that optimize the desired criteria. We show that the resulting options are non-trivial, intuitively meaningful, and useful for learning and planning.

André Barreto, Diana Borsa, John Quan et al.

The ability to transfer skills across tasks has the potential to scale up reinforcement learning (RL) agents to environments currently out of reach. Recently, a framework based on two ideas, successor features (SFs) and generalised policy improvement (GPI), has been introduced as a principled way of transferring skills. In this paper we extend the SFs & GPI framework in two ways. One of the basic assumptions underlying the original formulation of SFs & GPI is that rewards for all tasks of interest can be computed as linear combinations of a fixed set of features. We relax this constraint and show that the theoretical guarantees supporting the framework can be extended to any set of tasks that only differ in the reward function. Our second contribution is to show that one can use the reward functions themselves as features for future tasks, without any loss of expressiveness, thus removing the need to specify a set of features beforehand. This makes it possible to combine SFs & GPI with deep learning in a more stable way. We empirically verify this claim on a complex 3D environment where observations are images from a first-person perspective. We show that the transfer promoted by SFs & GPI leads to very good policies on unseen tasks almost instantaneously. We also describe how to learn policies specialised to the new tasks in a way that allows them to be added to the agent's set of skills, and thus be reused in the future.

Diana Borsa, André Barreto, John Quan et al.

The ability of a reinforcement learning (RL) agent to learn about many reward functions at the same time has many potential benefits, such as the decomposition of complex tasks into simpler ones, the exchange of information between tasks, and the reuse of skills. We focus on one aspect in particular, namely the ability to generalise to unseen tasks. Parametric generalisation relies on the interpolation power of a function approximator that is given the task description as input; one of its most common form are universal value function approximators (UVFAs). Another way to generalise to new tasks is to exploit structure in the RL problem itself. Generalised policy improvement (GPI) combines solutions of previous tasks into a policy for the unseen task; this relies on instantaneous policy evaluation of old policies under the new reward function, which is made possible through successor features (SFs). Our proposed universal successor features approximators (USFAs) combine the advantages of all of these, namely the scalability of UVFAs, the instant inference of SFs, and the strong generalisation of GPI. We discuss the challenges involved in training a USFA, its generalisation properties and demonstrate its practical benefits and transfer abilities on a large-scale domain in which the agent has to navigate in a first-person perspective three-dimensional environment.

Diana Borsa, Bilal Piot, Rémi Munos et al.

Observational learning is a type of learning that occurs as a function of observing, retaining and possibly replicating or imitating the behaviour of another agent. It is a core mechanism appearing in various instances of social learning and has been found to be employed in several intelligent species, including humans. In this paper, we investigate to what extent the explicit modelling of other agents is necessary to achieve observational learning through machine learning. Especially, we argue that observational learning can emerge from pure Reinforcement Learning (RL), potentially coupled with memory. Through simple scenarios, we demonstrate that an RL agent can leverage the information provided by the observations of an other agent performing a task in a shared environment. The other agent is only observed through the effect of its actions on the environment and never explicitly modeled. Two key aspects are borrowed from observational learning: i) the observer behaviour needs to change as a result of viewing a 'teacher' (another agent) and ii) the observer needs to be motivated somehow to engage in making use of the other agent's behaviour. The later is naturally modeled by RL, by correlating the learning agent's reward with the teacher agent's behaviour.

Diana Borsa, Thore Graepel, John Shawe-Taylor

We investigate a paradigm in multi-task reinforcement learning (MT-RL) in which an agent is placed in an environment and needs to learn to perform a series of tasks, within this space. Since the environment does not change, there is potentially a lot of common ground amongst tasks and learning to solve them individually seems extremely wasteful. In this paper, we explicitly model and learn this shared structure as it arises in the state-action value space. We will show how one can jointly learn optimal value-functions by modifying the popular Value-Iteration and Policy-Iteration procedures to accommodate this shared representation assumption and leverage the power of multi-task supervised learning. Finally, we demonstrate that the proposed model and training procedures, are able to infer good value functions, even under low samples regimes. In addition to data efficiency, we will show in our analysis, that learning abstractions of the state space jointly across tasks leads to more robust, transferable representations with the potential for better generalization. this shared representation assumption and leverage the power of multi-task supervised learning. Finally, we demonstrate that the proposed model and training procedures, are able to infer good value functions, even under low samples regimes. In addition to data efficiency, we will show in our analysis, that learning abstractions of the state space jointly across tasks leads to more robust, transferable representations with the potential for better generalization.

Diana Borsa, Thore Graepel, Andrew Gordon

We consider the problem of modelling noisy but highly symmetric shapes that can be viewed as hierarchies of whole-part relationships in which higher level objects are composed of transformed collections of lower level objects. To this end, we propose the stochastic wreath process, a fully generative probabilistic model of drawings. Following Leyton's "Generative Theory of Shape", we represent shapes as sequences of transformation groups composed through a wreath product. This representation emphasizes the maximization of transfer --- the idea that the most compact and meaningful representation of a given shape is achieved by maximizing the re-use of existing building blocks or parts. The proposed stochastic wreath process extends Leyton's theory by defining a probability distribution over geometric shapes in terms of noise processes that are aligned with the generative group structure of the shape. We propose an inference scheme for recovering the generative history of given images in terms of the wreath process using reversible jump Markov chain Monte Carlo methods and Approximate Bayesian Computation. In the context of sketching we demonstrate the feasibility and limitations of this approach on model-generated and real data.