J. Andrew Bagnell

Yuda Song, Yifei Zhou, Ayush Sekhari et al. · cmu

We consider a hybrid reinforcement learning setting (Hybrid RL), in which an agent has access to an offline dataset and the ability to collect experience via real-world online interaction. The framework mitigates the challenges that arise in both pure offline and online RL settings, allowing for the design of simple and highly effective algorithms, in both theory and practice. We demonstrate these advantages by adapting the classical Q learning/iteration algorithm to the hybrid setting, which we call Hybrid Q-Learning or Hy-Q. In our theoretical results, we prove that the algorithm is both computationally and statistically efficient whenever the offline dataset supports a high-quality policy and the environment has bounded bilinear rank. Notably, we require no assumptions on the coverage provided by the initial distribution, in contrast with guarantees for policy gradient/iteration methods. In our experimental results, we show that Hy-Q with neural network function approximation outperforms state-of-the-art online, offline, and hybrid RL baselines on challenging benchmarks, including Montezuma's Revenge.

Anirudh Vemula, Yuda Song, Aarti Singh et al. · cmu

We propose a novel approach to addressing two fundamental challenges in Model-based Reinforcement Learning (MBRL): the computational expense of repeatedly finding a good policy in the learned model, and the objective mismatch between model fitting and policy computation. Our "lazy" method leverages a novel unified objective, Performance Difference via Advantage in Model, to capture the performance difference between the learned policy and expert policy under the true dynamics. This objective demonstrates that optimizing the expected policy advantage in the learned model under an exploration distribution is sufficient for policy computation, resulting in a significant boost in computational efficiency compared to traditional planning methods. Additionally, the unified objective uses a value moment matching term for model fitting, which is aligned with the model's usage during policy computation. We present two no-regret algorithms to optimize the proposed objective, and demonstrate their statistical and computational gains compared to existing MBRL methods through simulated benchmarks.

Stephane Ross, Narek Melik-Barkhudarov, Kumar Shaurya Shankar et al.

Autonomous navigation for large Unmanned Aerial Vehicles (UAVs) is fairly straight-forward, as expensive sensors and monitoring devices can be employed. In contrast, obstacle avoidance remains a challenging task for Micro Aerial Vehicles (MAVs) which operate at low altitude in cluttered environments. Unlike large vehicles, MAVs can only carry very light sensors, such as cameras, making autonomous navigation through obstacles much more challenging. In this paper, we describe a system that navigates a small quadrotor helicopter autonomously at low altitude through natural forest environments. Using only a single cheap camera to perceive the environment, we are able to maintain a constant velocity of up to 1.5m/s. Given a small set of human pilot demonstrations, we use recent state-of-the-art imitation learning techniques to train a controller that can avoid trees by adapting the MAVs heading. We demonstrate the performance of our system in a more controlled environment indoors, and in real natural forest environments outdoors.

Gokul Swamy, Nived Rajaraman, Matthew Peng et al.

Online imitation learning is the problem of how best to mimic expert demonstrations, given access to the environment or an accurate simulator. Prior work has shown that in the infinite sample regime, exact moment matching achieves value equivalence to the expert policy. However, in the finite sample regime, even if one has no optimization error, empirical variance can lead to a performance gap that scales with $H^2 / N$ for behavioral cloning and $H / \sqrt{N}$ for online moment matching, where $H$ is the horizon and $N$ is the size of the expert dataset. We introduce the technique of replay estimation to reduce this empirical variance: by repeatedly executing cached expert actions in a stochastic simulator, we compute a smoother expert visitation distribution estimate to match. In the presence of general function approximation, we prove a meta theorem reducing the performance gap of our approach to the parameter estimation error for offline classification (i.e. learning the expert policy). In the tabular setting or with linear function approximation, our meta theorem shows that the performance gap incurred by our approach achieves the optimal $\widetilde{O} \left( \min({H^{3/2}} / {N}, {H} / {\sqrt{N}} \right)$ dependency, under significantly weaker assumptions compared to prior work. We implement multiple instantiations of our approach on several continuous control tasks and find that we are able to significantly improve policy performance across a variety of dataset sizes.

Gokul Swamy, Sanjiban Choudhury, J. Andrew Bagnell et al.

Inverse Reinforcement Learning (IRL) is a powerful set of techniques for imitation learning that aims to learn a reward function that rationalizes expert demonstrations. Unfortunately, traditional IRL methods suffer from a computational weakness: they require repeatedly solving a hard reinforcement learning (RL) problem as a subroutine. This is counter-intuitive from the viewpoint of reductions: we have reduced the easier problem of imitation learning to repeatedly solving the harder problem of RL. Another thread of work has proved that access to the side-information of the distribution of states where a strong policy spends time can dramatically reduce the sample and computational complexities of solving an RL problem. In this work, we demonstrate for the first time a more informed imitation learning reduction where we utilize the state distribution of the expert to alleviate the global exploration component of the RL subroutine, providing an exponential speedup in theory. In practice, we find that we are able to significantly speed up the prior art on continuous control tasks.

Gokul Swamy, Sanjiban Choudhury, J. Andrew Bagnell et al.

We consider imitation learning problems where the learner's ability to mimic the expert increases throughout the course of an episode as more information is revealed. One example of this is when the expert has access to privileged information: while the learner might not be able to accurately reproduce expert behavior early on in an episode, by considering the entire history of states and actions, they might be able to eventually identify the hidden context and act as the expert would. We prove that on-policy imitation learning algorithms (with or without access to a queryable expert) are better equipped to handle these sorts of asymptotically realizable problems than off-policy methods. This is because on-policy algorithms provably learn to recover from their initially suboptimal actions, while off-policy methods treat their suboptimal past actions as though they came from the expert. This often manifests as a latching behavior: a naive repetition of past actions. We conduct experiments in a toy bandit domain that show that there exist sharp phase transitions of whether off-policy approaches are able to match expert performance asymptotically, in contrast to the uniformly good performance of on-policy approaches. We demonstrate that on several continuous control tasks, on-policy approaches are able to use history to identify the context while off-policy approaches actually perform worse when given access to history.

Yuda Song, Lili Chen, Fahim Tajwar et al.

The success of RL for LLM post-training stems from an unreasonably uninformative source: a single bit of information per rollout as binary reward or preference label. At the other extreme, distillation offers dense supervision but requires demonstrations, which are costly and difficult to scale. We study text feedback as an intermediate signal: richer than scalar rewards, yet cheaper than complete demonstrations. Textual feedback is a natural mode of human interaction and is already abundant in many real-world settings, where users, annotators, and automated judges routinely critique LLM outputs. Towards leveraging text feedback at scale, we formalize a multi-turn RL setup, RL from Text Feedback (RLTF), where text feedback is available during training but not at inference. Therefore, models must learn to internalize the feedback in order to improve their test-time single-turn performance. To do this, we propose two methods: Self Distillation (RLTF-SD), which trains the single-turn policy to match its own feedback-conditioned second-turn generations; and Feedback Modeling (RLTF-FM), which predicts the feedback as an auxiliary objective. We provide theoretical analysis on both methods, and empirically evaluate on reasoning puzzles, competition math, and creative writing tasks. Our results show that both methods consistently outperform strong baselines across benchmarks, highlighting the potential of RL with an additional source of rich supervision at scale.

Gokul Swamy, Sanjiban Choudhury, J. Andrew Bagnell et al.

A variety of problems in econometrics and machine learning, including instrumental variable regression and Bellman residual minimization, can be formulated as satisfying a set of conditional moment restrictions (CMR). We derive a general, game-theoretic strategy for satisfying CMR that scales to nonlinear problems, is amenable to gradient-based optimization, and is able to account for finite sample uncertainty. We recover the approaches of Dikkala et al. and Dai et al. as special cases of our general framework before detailing various extensions and how to efficiently solve the game defined by CMR.

Zhaolin Gao, Jonathan D. Chang, Wenhao Zhan et al.

While originally developed for continuous control problems, Proximal Policy Optimization (PPO) has emerged as the work-horse of a variety of reinforcement learning (RL) applications, including the fine-tuning of generative models. Unfortunately, PPO requires multiple heuristics to enable stable convergence (e.g. value networks, clipping), and is notorious for its sensitivity to the precise implementation of these components. In response, we take a step back and ask what a minimalist RL algorithm for the era of generative models would look like. We propose REBEL, an algorithm that cleanly reduces the problem of policy optimization to regressing the relative reward between two completions to a prompt in terms of the policy, enabling strikingly lightweight implementation. In theory, we prove that fundamental RL algorithms like Natural Policy Gradient can be seen as variants of REBEL, which allows us to match the strongest known theoretical guarantees in terms of convergence and sample complexity in the RL literature. REBEL can also cleanly incorporate offline data and be extended to handle the intransitive preferences we frequently see in practice. Empirically, we find that REBEL provides a unified approach to language modeling and image generation with stronger or similar performance as PPO and DPO, all while being simpler to implement and more computationally efficient than PPO. When fine-tuning Llama-3-8B-Instruct, REBEL achieves strong performance in AlpacaEval 2.0, MT-Bench, and Open LLM Leaderboard.

Gokul Swamy, Sanjiban Choudhury, Wen Sun et al.

From a first-principles perspective, it may seem odd that the strongest results in foundation model fine-tuning (FT) are achieved via a relatively complex, two-stage training procedure. Specifically, one first trains a reward model (RM) on some dataset (e.g., human preferences) before using it to provide online feedback as part of a downstream reinforcement learning (RL) procedure, rather than directly optimizing the policy parameters on said dataset via offline maximum likelihood estimation. In fact, from an information-theoretic perspective, we can only lose information via passing through a reward model and cannot create any new information via on-policy sampling. To explain this discrepancy, we scrutinize several hypotheses on the value of RL in FT through both theoretical and empirical lenses. Of the hypotheses considered, we find the most support for the explanation that on problems with a generation-verification gap, (1) it is relatively easy to learn the relatively simple RM (verifier) from the preference data. Then, (2) the downstream RL procedure only returns policies (generators) that are optimal for such relatively simple verifiers. Thus, end-to-end, two-stage online FT only has to search over a reduced subset of the full space of policies, requiring less data than offline FT.

Juntao Ren, Gokul Swamy, Zhiwei Steven Wu et al.

The inverse reinforcement learning approach to imitation learning is a double-edged sword. On the one hand, it can enable learning from a smaller number of expert demonstrations with more robustness to error compounding than behavioral cloning approaches. On the other hand, it requires that the learner repeatedly solve a computationally expensive reinforcement learning (RL) problem. Often, much of this computation is wasted searching over policies very dissimilar to the expert's. In this work, we propose using hybrid RL -- training on a mixture of online and expert data -- to curtail unnecessary exploration. Intuitively, the expert data focuses the learner on good states during training, which reduces the amount of exploration required to compute a strong policy. Notably, such an approach doesn't need the ability to reset the learner to arbitrary states in the environment, a requirement of prior work in efficient inverse RL. More formally, we derive a reduction from inverse RL to expert-competitive RL (rather than globally optimal RL) that allows us to dramatically reduce interaction during the inner policy search loop while maintaining the benefits of the IRL approach. This allows us to derive both model-free and model-based hybrid inverse RL algorithms with strong policy performance guarantees. Empirically, we find that our approaches are significantly more sample efficient than standard inverse RL and several other baselines on a suite of continuous control tasks.

Yuda Song, Dhruv Rohatgi, Aarti Singh et al. · cmu

Partial observability is a notorious challenge in reinforcement learning (RL), due to the need to learn complex, history-dependent policies. Recent empirical successes have used privileged expert distillation--which leverages availability of latent state information during training (e.g., from a simulator) to learn and imitate the optimal latent, Markovian policy--to disentangle the task of "learning to see" from "learning to act". While expert distillation is more computationally efficient than RL without latent state information, it also has well-documented failure modes. In this paper--through a simple but instructive theoretical model called the perturbed Block MDP, and controlled experiments on challenging simulated locomotion tasks--we investigate the algorithmic trade-off between privileged expert distillation and standard RL without privileged information. Our main findings are: (1) The trade-off empirically hinges on the stochasticity of the latent dynamics, as theoretically predicted by contrasting approximate decodability with belief contraction in the perturbed Block MDP; and (2) The optimal latent policy is not always the best latent policy to distill. Our results suggest new guidelines for effectively exploiting privileged information, potentially advancing the efficiency of policy learning across many practical partially observable domains.

Yuda Song, J. Andrew Bagnell, Aarti Singh

We consider the hybrid reinforcement learning setting where the agent has access to both offline data and online interactive access. While Reinforcement Learning (RL) research typically assumes offline data contains complete action, reward and transition information, datasets with only state information (also known as observation-only datasets) are more general, abundant and practical. This motivates our study of the hybrid RL with observation-only offline dataset framework. While the task of competing with the best policy "covered" by the offline data can be solved if a reset model of the environment is provided (i.e., one that can be reset to any state), we show evidence of hardness when only given the weaker trace model (i.e., one can only reset to the initial states and must produce full traces through the environment), without further assumption of admissibility of the offline data. Under the admissibility assumptions -- that the offline data could actually be produced by the policy class we consider -- we propose the first algorithm in the trace model setting that provably matches the performance of algorithms that leverage a reset model. We also perform proof-of-concept experiments that suggest the effectiveness of our algorithm in practice.

Yuda Song, Gokul Swamy, Aarti Singh et al.

Learning from human preference data has emerged as the dominant paradigm for fine-tuning large language models (LLMs). The two most common families of techniques -- online reinforcement learning (RL) such as Proximal Policy Optimization (PPO) and offline contrastive methods such as Direct Preference Optimization (DPO) -- were positioned as equivalent in prior work due to the fact that both have to start from the same offline preference dataset. To further expand our theoretical understanding of the similarities and differences between online and offline techniques for preference fine-tuning, we conduct a rigorous analysis through the lens of dataset coverage, a concept that captures how the training data covers the test distribution and is widely used in RL. We prove that a global coverage condition is both necessary and sufficient for offline contrastive methods to converge to the optimal policy, but a weaker partial coverage condition suffices for online RL methods. This separation provides one explanation of why online RL methods can perform better than offline methods, especially when the offline preference data is not diverse enough. Finally, motivated by our preceding theoretical observations, we derive a hybrid preference optimization (HyPO) algorithm that uses offline data for contrastive-based preference optimization and online data for KL regularization. Theoretically and empirically, we demonstrate that HyPO is more performant than its pure offline counterpart DPO, while still preserving its computation and memory efficiency.

David Wu, Gokul Swamy, J. Andrew Bagnell et al.

Inverse Reinforcement Learning (IRL) is a powerful framework for learning complex behaviors from expert demonstrations. However, it traditionally requires repeatedly solving a computationally expensive reinforcement learning (RL) problem in its inner loop. It is desirable to reduce the exploration burden by leveraging expert demonstrations in the inner-loop RL. As an example, recent work resets the learner to expert states in order to inform the learner of high-reward expert states. However, such an approach is infeasible in the real world. In this work, we consider an alternative approach to speeding up the RL subroutine in IRL: \emph{pessimism}, i.e., staying close to the expert's data distribution, instantiated via the use of offline RL algorithms. We formalize a connection between offline RL and IRL, enabling us to use an arbitrary offline RL algorithm to improve the sample efficiency of IRL. We validate our theory experimentally by demonstrating a strong correlation between the efficacy of an offline RL algorithm and how well it works as part of an IRL procedure. By using a strong offline RL algorithm as part of an IRL procedure, we are able to find policies that match expert performance significantly more efficiently than the prior art.

Gokul Swamy, Sanjiban Choudhury, J. Andrew Bagnell et al.

We develop algorithms for imitation learning from policy data that was corrupted by temporally correlated noise in expert actions. When noise affects multiple timesteps of recorded data, it can manifest as spurious correlations between states and actions that a learner might latch on to, leading to poor policy performance. To break up these spurious correlations, we apply modern variants of the instrumental variable regression (IVR) technique of econometrics, enabling us to recover the underlying policy without requiring access to an interactive expert. In particular, we present two techniques, one of a generative-modeling flavor (DoubIL) that can utilize access to a simulator, and one of a game-theoretic flavor (ResiduIL) that can be run entirely offline. We find both of our algorithms compare favorably to behavioral cloning on simulated control tasks.

Anirudh Vemula, Wen Sun, Maxim Likhachev et al.

Iterative learning control (ILC) is a powerful technique for high performance tracking in the presence of modeling errors for optimal control applications. There is extensive prior work showing its empirical effectiveness in applications such as chemical reactors, industrial robots and quadcopters. However, there is little prior theoretical work that explains the effectiveness of ILC even in the presence of large modeling errors, where optimal control methods using the misspecified model (MM) often perform poorly. Our work presents such a theoretical study of the performance of both ILC and MM on Linear Quadratic Regulator (LQR) problems with unknown transition dynamics. We show that the suboptimality gap, as measured with respect to the optimal LQR controller, for ILC is lower than that for MM by higher order terms that become significant in the regime of high modeling errors. A key part of our analysis is the perturbation bounds for the discrete Ricatti equation in the finite horizon setting, where the solution is not a fixed point and requires tracking the error using recursive bounds. We back our theoretical findings with empirical experiments on a toy linear dynamical system with an approximate model, a nonlinear inverted pendulum system with misspecified mass, and a nonlinear planar quadrotor system in the presence of wind. Experiments show that ILC outperforms MM significantly, in terms of the cost of computed trajectories, when modeling errors are high.

Gokul Swamy, Sanjiban Choudhury, J. Andrew Bagnell et al.

Recent work by Jarrett et al. attempts to frame the problem of offline imitation learning (IL) as one of learning a joint energy-based model, with the hope of out-performing standard behavioral cloning. We suggest that notational issues obscure how the psuedo-state visitation distribution the authors propose to optimize might be disconnected from the policy's $\textit{true}$ state visitation distribution. We further construct natural examples where the parameter coupling advocated by Jarrett et al. leads to inconsistent estimates of the expert's policy, unlike behavioral cloning.

Gokul Swamy, Sanjiban Choudhury, J. Andrew Bagnell et al.

We provide a unifying view of a large family of previous imitation learning algorithms through the lens of moment matching. At its core, our classification scheme is based on whether the learner attempts to match (1) reward or (2) action-value moments of the expert's behavior, with each option leading to differing algorithmic approaches. By considering adversarially chosen divergences between learner and expert behavior, we are able to derive bounds on policy performance that apply for all algorithms in each of these classes, the first to our knowledge. We also introduce the notion of moment recoverability, implicit in many previous analyses of imitation learning, which allows us to cleanly delineate how well each algorithmic family is able to mitigate compounding errors. We derive three novel algorithm templates (AdVIL, AdRIL, and DAeQuIL) with strong guarantees, simple implementation, and competitive empirical performance.

Jonathan Spencer, Sanjiban Choudhury, Arun Venkatraman et al.

Imitation learning practitioners have often noted that conditioning policies on previous actions leads to a dramatic divergence between "held out" error and performance of the learner in situ. Interactive approaches can provably address this divergence but require repeated querying of a demonstrator. Recent work identifies this divergence as stemming from a "causal confound" in predicting the current action, and seek to ablate causal aspects of current state using tools from causal inference. In this work, we argue instead that this divergence is simply another manifestation of covariate shift, exacerbated particularly by settings of feedback between decisions and input features. The learner often comes to rely on features that are strongly predictive of decisions, but are subject to strong covariate shift. Our work demonstrates a broad class of problems where this shift can be mitigated, both theoretically and practically, by taking advantage of a simulator but without any further querying of expert demonstration. We analyze existing benchmarks used to test imitation learning approaches and find that these benchmarks are realizable and simple and thus insufficient for capturing the harder regimes of error compounding seen in real-world decision making problems. We find, in a surprising contrast with previous literature, but consistent with our theory, that naive behavioral cloning provides excellent results. We detail the need for new standardized benchmarks that capture the phenomena seen in robotics problems.

Anirudh Vemula, J. Andrew Bagnell, Maxim Likhachev

Given access to accurate dynamical models, modern planning approaches are effective in computing feasible and optimal plans for repetitive robotic tasks. However, it is difficult to model the true dynamics of the real world before execution, especially for tasks requiring interactions with objects whose parameters are unknown. A recent planning approach, CMAX, tackles this problem by adapting the planner online during execution to bias the resulting plans away from inaccurately modeled regions. CMAX, while being provably guaranteed to reach the goal, requires strong assumptions on the accuracy of the model used for planning and fails to improve the quality of the solution over repetitions of the same task. In this paper we propose CMAX++, an approach that leverages real-world experience to improve the quality of resulting plans over successive repetitions of a robotic task. CMAX++ achieves this by integrating model-free learning using acquired experience with model-based planning using the potentially inaccurate model. We provide provable guarantees on the completeness and asymptotic convergence of CMAX++ to the optimal path cost as the number of repetitions increases. CMAX++ is also shown to outperform baselines in simulated robotic tasks including 3D mobile robot navigation where the track friction is incorrectly modeled, and a 7D pick-and-place task where the mass of the object is unknown leading to discrepancy between true and modeled dynamics.

Anirudh Vemula, J. Andrew Bagnell

Trajectory optimization is an important tool for control and planning of complex, underactuated robots, and has shown impressive results in real world robotic tasks. However, in applications where the cost function to be optimized is non-smooth, modern trajectory optimization methods have extremely slow convergence. In this work, we present TRON, an iterative solver that can be used for efficient trajectory optimization in applications with non-smooth cost functions that are composed of smooth components. TRON achieves this by exploiting the structure of the objective to adaptively smooth the cost function, resulting in a sequence of objectives that can be efficiently optimized. TRON is provably guaranteed to converge to the global optimum of the non-smooth convex cost function when the dynamics are linear, and to a stationary point when the dynamics are nonlinear. Empirically, we show that TRON has faster convergence and lower final costs when compared to other trajectory optimization methods on a range of simulated tasks including collision-free motion planning for a mobile robot, sparse optimal control for surgical needle, and a satellite rendezvous problem.

Anirudh Vemula, Wen Sun, J. Andrew Bagnell

Parameter space exploration methods with black-box optimization have recently been shown to outperform state-of-the-art approaches in continuous control reinforcement learning domains. In this paper, we examine reasons why these methods work better and the situations in which they are worse than traditional action space exploration methods. Through a simple theoretical analysis, we show that when the parametric complexity required to solve the reinforcement learning problem is greater than the product of action space dimensionality and horizon length, exploration in action space is preferred. This is also shown empirically by comparing simple exploration methods on several toy problems.

Anirudh Vemula, Yash Oza, J. Andrew Bagnell et al.

Models used in modern planning problems to simulate outcomes of real world action executions are becoming increasingly complex, ranging from simulators that do physics-based reasoning to precomputed analytical motion primitives. However, robots operating in the real world often face situations not modeled by these models before execution. This imperfect modeling can lead to highly suboptimal or even incomplete behavior during execution. In this paper, we propose CMAX an approach for interleaving planning and execution. CMAX adapts its planning strategy online during real-world execution to account for any discrepancies in dynamics during planning, without requiring updates to the dynamics of the model. This is achieved by biasing the planner away from transitions whose dynamics are discovered to be inaccurately modeled, thereby leading to robot behavior that tries to complete the task despite having an inaccurate model. We provide provable guarantees on the completeness and efficiency of the proposed planning and execution framework under specific assumptions on the model, for both small and large state spaces. Our approach CMAX is shown to be efficient empirically in simulated robotic tasks including 4D planar pushing, and in real robotic experiments using PR2 involving a 3D pick-and-place task where the mass of the object is incorrectly modeled, and a 7D arm planning task where one of the joints is not operational leading to discrepancy in dynamics. The video of our physical robot experiments can be found at https://youtu.be/eQmAeWIhjO8

Wen Sun, Anirudh Vemula, Byron Boots et al.

We study Imitation Learning (IL) from Observations alone (ILFO) in large-scale MDPs. While most IL algorithms rely on an expert to directly provide actions to the learner, in this setting the expert only supplies sequences of observations. We design a new model-free algorithm for ILFO, Forward Adversarial Imitation Learning (FAIL), which learns a sequence of time-dependent policies by minimizing an Integral Probability Metric between the observation distributions of the expert policy and the learner. FAIL is the first provably efficient algorithm in ILFO setting, which learns a near-optimal policy with a number of samples that is polynomial in all relevant parameters but independent of the number of unique observations. The resulting theory extends the domain of provably sample efficient learning algorithms beyond existing results, which typically only consider tabular reinforcement learning settings or settings that require access to a near-optimal reset distribution. We also investigate the extension of FAIL in a model-based setting. Finally we demonstrate the efficacy of FAIL on multiple OpenAI Gym control tasks.

Anirudh Vemula, Wen Sun, J. Andrew Bagnell

Black-box optimizers that explore in parameter space have often been shown to outperform more sophisticated action space exploration methods developed specifically for the reinforcement learning problem. We examine these black-box methods closely to identify situations in which they are worse than action space exploration methods and those in which they are superior. Through simple theoretical analyses, we prove that complexity of exploration in parameter space depends on the dimensionality of parameter space, while complexity of exploration in action space depends on both the dimensionality of action space and horizon length. This is also demonstrated empirically by comparing simple exploration methods on several model problems, including Contextual Bandit, Linear Regression and Reinforcement Learning in continuous control.

Takayuki Osa, Joni Pajarinen, Gerhard Neumann et al.

As robots and other intelligent agents move from simple environments and problems to more complex, unstructured settings, manually programming their behavior has become increasingly challenging and expensive. Often, it is easier for a teacher to demonstrate a desired behavior rather than attempt to manually engineer it. This process of learning from demonstrations, and the study of algorithms to do so, is called imitation learning. This work provides an introduction to imitation learning. It covers the underlying assumptions, approaches, and how they relate; the rich set of algorithms developed to tackle the problem; and advice on effective tools and implementation. We intend this paper to serve two audiences. First, we want to familiarize machine learning experts with the challenges of imitation learning, particularly those arising in robotics, and the interesting theoretical and practical distinctions between it and more familiar frameworks like statistical supervised learning theory and reinforcement learning. Second, we want to give roboticists and experts in applied artificial intelligence a broader appreciation for the frameworks and tools available for imitation learning.

Wen Sun, J. Andrew Bagnell, Byron Boots

In this paper, we propose to combine imitation and reinforcement learning via the idea of reward shaping using an oracle. We study the effectiveness of the near-optimal cost-to-go oracle on the planning horizon and demonstrate that the cost-to-go oracle shortens the learner's planning horizon as function of its accuracy: a globally optimal oracle can shorten the planning horizon to one, leading to a one-step greedy Markov Decision Process which is much easier to optimize, while an oracle that is far away from the optimality requires planning over a longer horizon to achieve near-optimal performance. Hence our new insight bridges the gap and interpolates between imitation learning and reinforcement learning. Motivated by the above mentioned insights, we propose Truncated HORizon Policy Search (THOR), a method that focuses on searching for policies that maximize the total reshaped reward over a finite planning horizon when the oracle is sub-optimal. We experimentally demonstrate that a gradient-based implementation of THOR can achieve superior performance compared to RL baselines and IL baselines even when the oracle is sub-optimal.

Wen Sun, Geoffrey J. Gordon, Byron Boots et al.

Recently, a novel class of Approximate Policy Iteration (API) algorithms have demonstrated impressive practical performance (e.g., ExIt from [2], AlphaGo-Zero from [27]). This new family of algorithms maintains, and alternately optimizes, two policies: a fast, reactive policy (e.g., a deep neural network) deployed at test time, and a slow, non-reactive policy (e.g., Tree Search), that can plan multiple steps ahead. The reactive policy is updated under supervision from the non-reactive policy, while the non-reactive policy is improved with guidance from the reactive policy. In this work we study this Dual Policy Iteration (DPI) strategy in an alternating optimization framework and provide a convergence analysis that extends existing API theory. We also develop a special instance of this framework which reduces the update of non-reactive policies to model-based optimal control using learned local models, and provides a theoretically sound way of unifying model-free and model-based RL approaches with unknown dynamics. We demonstrate the efficacy of our approach on various continuous control Markov Decision Processes.

Hanzhang Hu, Debadeepta Dey, Allison Del Giorno et al.

Skip connections are increasingly utilized by deep neural networks to improve accuracy and cost-efficiency. In particular, the recent DenseNet is efficient in computation and parameters, and achieves state-of-the-art predictions by directly connecting each feature layer to all previous ones. However, DenseNet's extreme connectivity pattern may hinder its scalability to high depths, and in applications like fully convolutional networks, full DenseNet connections are prohibitively expensive. This work first experimentally shows that one key advantage of skip connections is to have short distances among feature layers during backpropagation. Specifically, using a fixed number of skip connections, the connection patterns with shorter backpropagation distance among layers have more accurate predictions. Following this insight, we propose a connection template, Log-DenseNet, which, in comparison to DenseNet, only slightly increases the backpropagation distances among layers from 1 to ($1 + \log_2 L$), but uses only $L\log_2 L$ total connections instead of $O(L^2)$. Hence, Log-DenseNets are easier than DenseNets to implement and to scale. We demonstrate the effectiveness of our design principle by showing better performance than DenseNets on tabula rasa semantic segmentation, and competitive results on visual recognition.

Arun Venkatraman, Nicholas Rhinehart, Wen Sun et al.

Recurrent neural networks (RNNs) are a vital modeling technique that rely on internal states learned indirectly by optimization of a supervised, unsupervised, or reinforcement training loss. RNNs are used to model dynamic processes that are characterized by underlying latent states whose form is often unknown, precluding its analytic representation inside an RNN. In the Predictive-State Representation (PSR) literature, latent state processes are modeled by an internal state representation that directly models the distribution of future observations, and most recent work in this area has relied on explicitly representing and targeting sufficient statistics of this probability distribution. We seek to combine the advantages of RNNs and PSRs by augmenting existing state-of-the-art recurrent neural networks with Predictive-State Decoders (PSDs), which add supervision to the network's internal state representation to target predicting future observations. Predictive-State Decoders are simple to implement and easily incorporated into existing training pipelines via additional loss regularization. We demonstrate the effectiveness of PSDs with experimental results in three different domains: probabilistic filtering, Imitation Learning, and Reinforcement Learning. In each, our method improves statistical performance of state-of-the-art recurrent baselines and does so with fewer iterations and less data.

Allison Del Giorno, J. Andrew Bagnell, Martial Hebert

In the anomaly detection setting, the native feature embedding can be a crucial source of bias. We present a technique, Feature Omission using Context in Unsupervised Settings (FOCUS) to learn a feature mapping that is invariant to changes exemplified in training sets while retaining as much descriptive power as possible. While this method could apply to many unsupervised settings, we focus on applications in anomaly detection, where little task-labeled data is available. Our algorithm requires only non-anomalous sets of data, and does not require that the contexts in the training sets match the context of the test set. By maximizing within-set variance and minimizing between-set variance, we are able to identify and remove distracting features while retaining fidelity to the descriptiveness needed at test time. In the linear case, our formulation reduces to a generalized eigenvalue problem that can be solved quickly and applied to test sets outside the context of the training sets. This technique allows us to align technical definitions of anomaly detection with human definitions through appropriate mappings of the feature space. We demonstrate that this method is able to remove uninformative parts of the feature space for the anomaly detection setting.

Hanzhang Hu, Debadeepta Dey, Martial Hebert et al.

This work considers the trade-off between accuracy and test-time computational cost of deep neural networks (DNNs) via \emph{anytime} predictions from auxiliary predictions. Specifically, we optimize auxiliary losses jointly in an \emph{adaptive} weighted sum, where the weights are inversely proportional to average of each loss. Intuitively, this balances the losses to have the same scale. We demonstrate theoretical considerations that motivate this approach from multiple viewpoints, including connecting it to optimizing the geometric mean of the expectation of each loss, an objective that ignores the scale of losses. Experimentally, the adaptive weights induce more competitive anytime predictions on multiple recognition data-sets and models than non-adaptive approaches including weighing all losses equally. In particular, anytime neural networks (ANNs) can achieve the same accuracy faster using adaptive weights on a small network than using static constant weights on a large one. For problems with high performance saturation, we also show a sequence of exponentially deepening ANNscan achieve near-optimal anytime results at any budget, at the cost of a const fraction of extra computation.

Shervin Javdani, Henny Admoni, Stefania Pellegrinelli et al.

In shared autonomy, a user and autonomous system work together to achieve shared goals. To collaborate effectively, the autonomous system must know the user's goal. As such, most prior works follow a predict-then-act model, first predicting the user's goal with high confidence, then assisting given that goal. Unfortunately, confidently predicting the user's goal may not be possible until they have nearly achieved it, causing predict-then-act methods to provide little assistance. However, the system can often provide useful assistance even when confidence for any single goal is low (e.g. move towards multiple goals). In this work, we formalize this insight by modelling shared autonomy as a Partially Observable Markov Decision Process (POMDP), providing assistance that minimizes the expected cost-to-go with an unknown goal. As solving this POMDP optimally is intractable, we use hindsight optimization to approximate. We apply our framework to both shared-control teleoperation and human-robot teaming. Compared to predict-then-act methods, our method achieves goals faster, requires less user input, decreases user idling time, and results in fewer user-robot collisions.

Jiaji Zhou, J. Andrew Bagnell, Matthew T. Mason

Based on the convex force-motion polynomial model for quasi-static sliding, we derive the kinematic contact model to determine the contact modes and instantaneous object motion on a supporting surface given a position controlled manipulator. The inherently stochastic object-to-surface friction distribution is modelled by sampling physically consistent parameters from appropriate distributions, with only one parameter to control the amount of noise. Thanks to the high fidelity and smoothness of convex polynomial models, the mechanics of patch contact is captured while being computationally efficient without mode selection at support points. The motion equations for both single and multiple frictional contacts are given. Simulation based on the model is validated with robotic pushing and grasping experiments.

Wen Sun, Arun Venkatraman, Geoffrey J. Gordon et al.

Researchers have demonstrated state-of-the-art performance in sequential decision making problems (e.g., robotics control, sequential prediction) with deep neural network models. One often has access to near-optimal oracles that achieve good performance on the task during training. We demonstrate that AggreVaTeD --- a policy gradient extension of the Imitation Learning (IL) approach of (Ross & Bagnell, 2014) --- can leverage such an oracle to achieve faster and better solutions with less training data than a less-informed Reinforcement Learning (RL) technique. Using both feedforward and recurrent neural network predictors, we present stochastic gradient procedures on a sequential prediction task, dependency-parsing from raw image data, as well as on various high dimensional robotics control problems. We also provide a comprehensive theoretical study of IL that demonstrates we can expect up to exponentially lower sample complexity for learning with AggreVaTeD than with RL algorithms, which backs our empirical findings. Our results and theory indicate that the proposed approach can achieve superior performance with respect to the oracle when the demonstrator is sub-optimal.

Hanzhang Hu, Wen Sun, Arun Venkatraman et al.

Boosting is a popular ensemble algorithm that generates more powerful learners by linearly combining base models from a simpler hypothesis class. In this work, we investigate the problem of adapting batch gradient boosting for minimizing convex loss functions to online setting where the loss at each iteration is i.i.d sampled from an unknown distribution. To generalize from batch to online, we first introduce the definition of online weak learning edge with which for strongly convex and smooth loss functions, we present an algorithm, Streaming Gradient Boosting (SGB) with exponential shrinkage guarantees in the number of weak learners. We further present an adaptation of SGB to optimize non-smooth loss functions, for which we derive a O(ln N/N) convergence rate. We also show that our analysis can extend to adversarial online learning setting under a stronger assumption that the online weak learning edge will hold in adversarial setting. We finally demonstrate experimental results showing that in practice our algorithms can achieve competitive results as classic gradient boosting while using less computation.

Allison Del Giorno, J. Andrew Bagnell, Martial Hebert

We address an anomaly detection setting in which training sequences are unavailable and anomalies are scored independently of temporal ordering. Current algorithms in anomaly detection are based on the classical density estimation approach of learning high-dimensional models and finding low-probability events. These algorithms are sensitive to the order in which anomalies appear and require either training data or early context assumptions that do not hold for longer, more complex videos. By defining anomalies as examples that can be distinguished from other examples in the same video, our definition inspires a shift in approaches from classical density estimation to simple discriminative learning. Our contributions include a novel framework for anomaly detection that is (1) independent of temporal ordering of anomalies, and (2) unsupervised, requiring no separate training sequences. We show that our algorithm can achieve state-of-the-art results even when we adjust the setting by removing training sequences from standard datasets.

Shreyansh Daftry, J. Andrew Bagnell, Martial Hebert

The ability to transfer knowledge gained in previous tasks into new contexts is one of the most important mechanisms of human learning. Despite this, adapting autonomous behavior to be reused in partially similar settings is still an open problem in current robotics research. In this paper, we take a small step in this direction and propose a generic framework for learning transferable motion policies. Our goal is to solve a learning problem in a target domain by utilizing the training data in a different but related source domain. We present this in the context of an autonomous MAV flight using monocular reactive control, and demonstrate the efficacy of our proposed approach through extensive real-world flight experiments in outdoor cluttered environments.

Shreyansh Daftry, Sam Zeng, J. Andrew Bagnell et al.

As robots aspire for long-term autonomous operations in complex dynamic environments, the ability to reliably take mission-critical decisions in ambiguous situations becomes critical. This motivates the need to build systems that have situational awareness to assess how qualified they are at that moment to make a decision. We call this self-evaluating capability as introspection. In this paper, we take a small step in this direction and propose a generic framework for introspective behavior in perception systems. Our goal is to learn a model to reliably predict failures in a given system, with respect to a task, directly from input sensor data. We present this in the context of vision-based autonomous MAV flight in outdoor natural environments, and show that it effectively handles uncertain situations.

Shreyansh Daftry, Sam Zeng, Arbaaz Khan et al.

Recently, there have been numerous advances in the development of biologically inspired lightweight Micro Aerial Vehicles (MAVs). While autonomous navigation is fairly straight-forward for large UAVs as expensive sensors and monitoring devices can be employed, robust methods for obstacle avoidance remains a challenging task for MAVs which operate at low altitude in cluttered unstructured environments. Due to payload and power constraints, it is necessary for such systems to have autonomous navigation and flight capabilities using mostly passive sensors such as cameras. In this paper, we describe a robust system that enables autonomous navigation of small agile quad-rotors at low altitude through natural forest environments. We present a direct depth estimation approach that is capable of producing accurate, semi-dense depth-maps in real time. Furthermore, a novel wind-resistant control scheme is presented that enables stable way-point tracking even in the presence of strong winds. We demonstrate the performance of our system through extensive experiments on real images and field tests in a cluttered outdoor environment.

Jiaji Zhou, Robert Paolini, J. Andrew Bagnell et al.

We propose a polynomial force-motion model for planar sliding. The set of generalized friction loads is the 1-sublevel set of a polynomial whose gradient directions correspond to generalized velocities. Additionally, the polynomial is confined to be convex even-degree homogeneous in order to obey the maximum work inequality, symmetry, shape invariance in scale, and fast invertibility. We present a simple and statistically-efficient model identification procedure using a sum-of-squares convex relaxation. Simulation and robotic experiments validate the accuracy and efficiency of our approach. We also show practical applications of our model including stable pushing of objects and free sliding dynamic simulations.

Wen Sun, Arun Venkatraman, Byron Boots et al.

Latent state space models are a fundamental and widely used tool for modeling dynamical systems. However, they are difficult to learn from data and learned models often lack performance guarantees on inference tasks such as filtering and prediction. In this work, we present the PREDICTIVE STATE INFERENCE MACHINE (PSIM), a data-driven method that considers the inference procedure on a dynamical system as a composition of predictors. The key idea is that rather than first learning a latent state space model, and then using the learned model for inference, PSIM directly learns predictors for inference in predictive state space. We provide theoretical guarantees for inference, in both realizable and agnostic settings, and showcase practical performance on a variety of simulated and real world robotics benchmarks.

Shervin Javdani, Siddhartha S. Srinivasa, J. Andrew Bagnell

In shared autonomy, user input and robot autonomy are combined to control a robot to achieve a goal. Often, the robot does not know a priori which goal the user wants to achieve, and must both predict the user's intended goal, and assist in achieving that goal. We formulate the problem of shared autonomy as a Partially Observable Markov Decision Process with uncertainty over the user's goal. We utilize maximum entropy inverse optimal control to estimate a distribution over the user's goal based on the history of inputs. Ideally, the robot assists the user by solving for an action which minimizes the expected cost-to-go for the (unknown) goal. As solving the POMDP to select the optimal action is intractable, we use hindsight optimization to approximate the solution. In a user study, we compare our method to a standard predict-then-blend approach. We find that our method enables users to accomplish tasks more quickly while utilizing less input. However, when asked to rate each system, users were mixed in their assessment, citing a tradeoff between maintaining control authority and accomplishing tasks quickly.

Katharina Muelling, Arun Venkatraman, Jean-Sebastien Valois et al.

Robot teleoperation systems face a common set of challenges including latency, low-dimensional user commands, and asymmetric control inputs. User control with Brain-Computer Interfaces (BCIs) exacerbates these problems through especially noisy and erratic low-dimensional motion commands due to the difficulty in decoding neural activity. We introduce a general framework to address these challenges through a combination of computer vision, user intent inference, and arbitration between the human input and autonomous control schemes. Adjustable levels of assistance allow the system to balance the operator's capabilities and feelings of comfort and control while compensating for a task's difficulty. We present experimental results demonstrating significant performance improvement using the shared-control assistance framework on adapted rehabilitation benchmarks with two subjects implanted with intracortical brain-computer interfaces controlling a seven degree-of-freedom robotic manipulator as a prosthetic. Our results further indicate that shared assistance mitigates perceived user difficulty and even enables successful performance on previously infeasible tasks. We showcase the extensibility of our architecture with applications to quality-of-life tasks such as opening a door, pouring liquids from containers, and manipulation with novel objects in densely cluttered environments.

Kevin Waugh, Dustin Morrill, J. Andrew Bagnell et al.

We propose a novel online learning method for minimizing regret in large extensive-form games. The approach learns a function approximator online to estimate the regret for choosing a particular action. A no-regret algorithm uses these estimates in place of the true regrets to define a sequence of policies. We prove the approach sound by providing a bound relating the quality of the function approximation and regret of the algorithm. A corollary being that the method is guaranteed to converge to a Nash equilibrium in self-play so long as the regrets are ultimately realizable by the function approximator. Our technique can be understood as a principled generalization of existing work on abstraction in large games; in our work, both the abstraction as well as the equilibrium are learned during self-play. We demonstrate empirically the method achieves higher quality strategies than state-of-the-art abstraction techniques given the same resources.

Debadeepta Dey, Kumar Shaurya Shankar, Sam Zeng et al.

Cameras provide a rich source of information while being passive, cheap and lightweight for small and medium Unmanned Aerial Vehicles (UAVs). In this work we present the first implementation of receding horizon control, which is widely used in ground vehicles, with monocular vision as the only sensing mode for autonomous UAV flight in dense clutter. We make it feasible on UAVs via a number of contributions: novel coupling of perception and control via relevant and diverse, multiple interpretations of the scene around the robot, leveraging recent advances in machine learning to showcase anytime budgeted cost-sensitive feature selection, and fast non-linear regression for monocular depth prediction. We empirically demonstrate the efficacy of our novel pipeline via real world experiments of more than 2 kms through dense trees with a quadrotor built from off-the-shelf parts. Moreover our pipeline is designed to combine information from other modalities like stereo and lidar as well if available.

Kevin Waugh, J. Andrew Bagnell

The task of computing approximate Nash equilibria in large zero-sum extensive-form games has received a tremendous amount of attention due mainly to the Annual Computer Poker Competition. Immediately after its inception, two competing and seemingly different approaches emerged---one an application of no-regret online learning, the other a sophisticated gradient method applied to a convex-concave saddle-point formulation. Since then, both approaches have grown in relative isolation with advancements on one side not effecting the other. In this paper, we rectify this by dissecting and, in a sense, unify the two views.

Nicholas Rhinehart, Jiaji Zhou, Martial Hebert et al.

We consider detecting objects in an image by iteratively selecting from a set of arbitrarily shaped candidate regions. Our generic approach, which we term visual chunking, reasons about the locations of multiple object instances in an image while expressively describing object boundaries. We design an optimization criterion for measuring the performance of a list of such detections as a natural extension to a common per-instance metric. We present an efficient algorithm with provable performance for building a high-quality list of detections from any candidate set of region-based proposals. We also develop a simple class-specific algorithm to generate a candidate region instance in near-linear time in the number of low-level superpixels that outperforms other region generating methods. In order to make predictions on novel images at testing time without access to ground truth, we develop learning approaches to emulate these algorithms' behaviors. We demonstrate that our new approach outperforms sophisticated baselines on benchmark datasets.

Hanzhang Hu, Alexander Grubb, J. Andrew Bagnell et al.

We consider \textit{anytime} linear prediction in the common machine learning setting, where features are in groups that have costs. We achieve anytime (or interruptible) predictions by sequencing the computation of feature groups and reporting results using the computed features at interruption. We extend Orthogonal Matching Pursuit (OMP) and Forward Regression (FR) to learn the sequencing greedily under this group setting with costs. We theoretically guarantee that our algorithms achieve near-optimal linear predictions at each budget when a feature group is chosen. With a novel analysis of OMP, we improve its theoretical bound to the same strength as that of FR. In addition, we develop a novel algorithm that consumes cost $4B$ to approximate the optimal performance of \textit{any} cost $B$, and prove that with cost less than $4B$, such an approximation is impossible. To our knowledge, these are the first anytime bounds at \textit{all} budgets. We test our algorithms on two real-world data-sets and evaluate them in terms of anytime linear prediction performance against cost-weighted Group Lasso and alternative greedy algorithms.