The Successor Representation, $\gamma$-Models,
and Infinite-Horizon Prediction


The Successor Representation, Gamma-Models, and Infinite-Horizon Prediction

Standard single-step models have a horizon of one. This post describes a method for training predictive dynamics models in continuous state spaces with an infinite, probabilistic horizon.

Reinforcement learning algorithms are frequently categorized by whether they predict future states at any point in their decision-making process. Those that do are called model-based, and those that do not are dubbed model-free. This classification is so common that we mostly take it for granted these days; I am guilty of using it myself. However, this distinction is not as clear-cut as it may initially seem.

In this post, I will talk about an alternative view that emphases the mechanism of prediction instead of the content of prediction. This shift in focus brings into relief a space between model-based and model-free methods that contains exciting directions for reinforcement learning. The first half of this post describes some of the classic tools in this space, including generalized value functions and the successor representation. The latter half is based on our recent paper about infinite-horizon predictive models, for which code is available here.


Does GPT-2 Know Your Phone Number?


Most likely not.

Yet, OpenAI’s GPT-2 language model does know how to reach a certain Peter W--- (name redacted for privacy). When prompted with a short snippet of Internet text, the model accurately generates Peter’s contact information, including his work address, email, phone, and fax:

In our recent paper, we evaluate how large language models memorize and regurgitate such rare snippets of their training data. We focus on GPT-2 and find that at least 0.1% of its text generations (a very conservative estimate) contain long verbatim strings that are “copy-pasted” from a document in its training set.

Such memorization would be an obvious issue for language models that are trained on private data, e.g., on users’ emails, as the model might inadvertently output a user’s sensitive conversations. Yet, even for models that are trained on public data from the Web (e.g., GPT-2, GPT-3, T5, RoBERTa, TuringNLG), memorization of training data raises multiple challenging regulatory questions, ranging from misuse of personally identifiable information to copyright infringement.


Offline Reinforcement Learning: How Conservative Algorithms Can Enable New Applications


Deep reinforcement learning has made significant progress in the last few years, with success stories in robotic control, game playing and science problems. While RL methods present a general paradigm where an agent learns from its own interaction with an environment, this requirement for “active” data collection is also a major hindrance in the application of RL methods to real-world problems, since active data collection is often expensive and potentially unsafe. An alternative “data-driven” paradigm of RL, referred to as offline RL (or batch RL) has recently regained popularity as a viable path towards effective real-world RL. As shown in the figure below, offline RL requires learning skills solely from previously collected datasets, without any active environment interaction. It provides a way to utilize previously collected datasets from a variety of sources, including human demonstrations, prior experiments, domain-specific solutions and even data from different but related problems, to build complex decision-making engines.


Learning State Abstractions for Long-Horizon Planning


Many tasks that we do on a regular basis, such as navigating a city, cooking a meal, or loading a dishwasher, require planning over extended periods of time. Accomplishing these tasks may seem simple to us; however, reasoning over long time horizons remains a major challenge for today’s Reinforcement Learning (RL) algorithms. While unable to plan over long horizons, deep RL algorithms excel at learning policies for short horizon tasks, such as robotic grasping, directly from pixels. At the same time, classical planning methods such as Dijkstra’s algorithm and A$^*$ search can plan over long time horizons, but they require hand-specified or task-specific abstract representations of the environment as input.

To achieve the best of both worlds, state-of-the-art visual navigation methods have applied classical search methods to learned graphs. In particular, SPTM [2] and SoRB [3] use a replay buffer of observations as nodes in a graph and learn a parametric distance function to draw edges in the graph. These methods have been successfully applied to long-horizon simulated navigation tasks that were too challenging for previous methods to solve.


EvolveGraph: Dynamic Neural Relational Reasoning for Interacting Systems


Multi-agent interacting systems are prevalent in the world, from purely physical systems to complicated social dynamic systems. The interactions between entities / components can give rise to very complex behavior patterns at the level of both individuals and the multi-agent system as a whole. Since usually only the trajectories of individual entities are observed without any knowledge of the underlying interaction patterns, and there are usually multiple possible modalities for each agent with uncertainty, it is challenging to model their dynamics and forecast their future behaviors.

Figure 1. Typical multi-agent interacting systems.

In many real-world applications (e.g. autonomous vehicles, mobile robots), an effective understanding of the situation and accurate trajectory prediction of interactive agents play a significant role in downstream tasks, such as decision making and planning. We introduce a generic trajectory forecasting framework (named EvolveGraph) with explicit relational structure recognition and prediction via latent interaction graphs among multiple heterogeneous, interactive agents. Considering the uncertainty of future behaviors, the model is designed to provide multi-modal prediction hypotheses. Since the underlying interactions may evolve even with abrupt changes over time, and different modalities of evolution may lead to different outcomes, we address the necessity of dynamic relational reasoning and adaptively evolving the interaction graphs.


Training on Test Inputs with Amortized Conditional Normalized Maximum Likelihood


Current machine learning methods provide unprecedented accuracy across a range of domains, from computer vision to natural language processing. However, in many important high-stakes applications, such as medical diagnosis or autonomous driving, rare mistakes can be extremely costly, and thus effective deployment of learned models requires not only high accuracy, but also a way to measure the certainty in a model’s predictions. Reliable uncertainty quantification is especially important when faced with out-of-distribution inputs, as model accuracy tends to degrade heavily on inputs that differ significantly from those seen during training. In this blog post, we will discuss how we can get reliable uncertainty estimation with a strategy that does not simply rely on a learned model to extrapolate to out-of-distribution inputs, but instead asks: “given my training data, which labels would make sense for this input?”.


Goodhart’s Law, Diversity and a Series of Seemingly Unrelated Toy Problems


Goodhart’s Law is an adage which states the following:

“When a measure becomes a target, it ceases to be a good measure.”

This is particularly pertinent in machine learning, where the source of many of our greatest achievements comes from optimizing a target in the form of a loss function. The most prominent way to do so is with stochastic gradient descent (SGD), which applies a simple rule, follow the gradient:

\[\theta_{t+1} = \theta_t - \alpha \nabla_\theta \mathcal{L}(\theta_t)\]

For some step size $\alpha$. Updates of this form have led to a series of breakthroughs from computer vision to reinforcement learning, and it is easy to see why it is so popular: 1) it is relatively cheap to compute using backprop 2) it is guaranteed to locally reduce the loss at every step and finally 3) it has an amazing track record empirically.


Adapting on the Fly to Test Time Distribution Shift


Imagine that you are building the next generation machine learning model for handwriting transcription. Based on previous iterations of your product, you have identified a key challenge for this rollout: after deployment, new end users often have different and unseen handwriting styles, leading to distribution shift. One solution for this challenge is to learn an adaptive model that can specialize and adjust to each user’s handwriting style over time. This solution seems promising, but it must be balanced against concerns about ease of use: requiring users to provide feedback to the model may be cumbersome and hinder adoption. Is it possible instead to learn a model that can adapt to new users without labels?


Reinforcement learning is supervised learning on optimized data


The two most common perspectives on Reinforcement learning (RL) are optimization and dynamic programming. Methods that compute the gradients of the non-differentiable expected reward objective, such as the REINFORCE trick are commonly grouped into the optimization perspective, whereas methods that employ TD-learning or Q-learning are dynamic programming methods. While these methods have shown considerable success in recent years, these methods are still quite challenging to apply to new problems. In contrast deep supervised learning has been extremely successful and we may hence ask: Can we use supervised learning to perform RL?

In this blog post we discuss a mental model for RL, based on the idea that RL can be viewed as doing supervised learning on the “good data”. What makes RL challenging is that, unless you’re doing imitation learning, actually acquiring that “good data” is quite challenging. Therefore, RL might be viewed as a joint optimization problem over both the policy and the data. Seen from this supervised learning perspective, many RL algorithms can be viewed as alternating between finding good data and doing supervised learning on that data. It turns out that finding “good data” is much easier in the multi-task setting, or settings that can be converted to a different problem for which obtaining “good data” is easy. In fact, we will discuss how techniques such as hindsight relabeling and inverse RL can be viewed as optimizing data.


Plan2Explore: Active Model-Building for Self-Supervised Visual Reinforcement Learning


This post is cross-listed on the CMU ML blog.

To operate successfully in unstructured open-world environments, autonomous intelligent agents need to solve many different tasks and learn new tasks quickly. Reinforcement learning has enabled artificial agents to solve complex tasks both in simulation and real-world. However, it requires collecting large amounts of experience in the environment, and the agent learns only that particular task, much like a student memorizing a lecture without understanding. Self-supervised reinforcement learning has emerged as an alternative, where the agent only follows an intrinsic objective that is independent of any individual task, analogously to unsupervised representation learning. After experimenting with the environment without supervision, the agent builds an understanding of the environment, which enables it to adapt to specific downstream tasks more efficiently.

In this post, we explain our recent publication that develops Plan2Explore. While many recent papers on self-supervised reinforcement learning have focused on model-free agents that can only capture knowledge by remembering behaviors practiced during self-supervision, our agent learns an internal world model that lets it extrapolate beyond memorized facts by predicting what will happen as a consequence of different potential actions. The world model captures general knowledge, allowing Plan2Explore to quickly solve new tasks through planning in its own imagination. In contrast to the model-free prior work, the world model further enables the agent to explore what it expects to be novel, rather than repeating what it found novel in the past. Plan2Explore obtains state-of-the-art zero-shot and few-shot performance on continuous control benchmarks with high-dimensional input images. To make it easy to experiment with our agent, we are open-sourcing the complete source code.