Explaining Fast Improvement in Online Policy Optimization

Online policy optimization (OPO) views policy optimization for sequential decision making as an online learning problem. In this framework, the algorithm designer defines a sequence of online loss functions such that the regret rate in online learning implies the policy convergence rate and the minimal loss witnessed by the policy class determines the policy performance bias. This reduction technique has been successfully applied to solving various policy optimization problems, including imitation learning, structured prediction, and system identification. Interestingly, the policy improvement speed observed in practice is usually much faster than existing theory suggests. In this work, we provide an explanation of this fast policy improvement phenomenon. Let $\epsilon$ denote the policy class bias and assume the online loss functions are convex, smooth, and non-negative. We prove that, after $N$ rounds of OPO with stochastic feedback, the policy converges in $\tilde{O}(1/N + \sqrt{\epsilon/N})$ in both expectation and high probability. In other words, we show that adopting a sufficiently expressive policy class in OPO has two benefits: both the convergence rate increases and the performance bias decreases, as the policy class becomes reasonably rich. This new theoretical insight is further verified in an online imitation learning experiment.

Euclideanizing Flows: Diffeomorphic Reduction for Learning Stable Dynamical Systems

Robotic tasks often require motions with complex geometric structures. We present an approach to learn such motions from a limited number of human demonstrations by exploiting the regularity properties of human motions e.g. stability, smoothness, and boundedness. The complex motions are encoded as rollouts of a stable dynamical system, which, under a change of coordinates defined by a diffeomorphism, is equivalent to a simple, hand-specified dynamical system. As an immediate result of using diffeomorphisms, the stability property of the hand-specified dynamical system directly carry over to the learned dynamical system. Inspired by recent works in density estimation, we propose to represent the diffeomorphism as a composition of simple parameterized diffeomorphisms. Additional structure is imposed to provide guarantees on the smoothness of the generated motions. The efficacy of this approach is demonstrated through validation on an established benchmark as well demonstrations collected on a real-world robotic system.

In Defense of Graph Inference Algorithms for Weakly Supervised Object Localization

Weakly Supervised Object Localization (WSOL) methods have become increasingly popular since they only require image level labels as opposed to expensive bounding box annotations required by fully supervised algorithms. Typically, a WSOL model is first trained to predict class generic objectness scores on an off-the-shelf fully supervised source dataset and then it is progressively adapted to learn the objects in the weakly supervised target dataset. In this work, we argue that learning only an objectness function is a weak form of knowledge transfer and propose to learn a classwise pairwise similarity function that directly compares two input proposals as well. The combined localization model and the estimated object annotations are jointly learned in an alternating optimization paradigm as is typically done in standard WSOL methods. In contrast to the existing work that learns pairwise similarities, our proposed approach optimizes a unified objective with convergence guarantee and it is computationally efficient for large-scale applications. Experiments on the COCO and ILSVRC 2013 detection datasets show that the performance of the localization model improves significantly with the inclusion of pairwise similarity function. For instance, in the ILSVRC dataset, the Correct Localization (CorLoc) performance improves from 72.7% to 78.2% which is a new state-of-the-art for weakly supervised object localization task.

Intra Order-preserving Functions for Calibration of Multi-Class Neural Networks

Predicting calibrated confidence scores for multi-class deep networks is important for avoiding rare but costly mistakes. A common approach is to learn a post-hoc calibration function that transforms the output of the original network into calibrated confidence scores while maintaining the network's accuracy. However, previous post-hoc calibration techniques work only with simple calibration functions, potentially lacking sufficient representation to calibrate the complex function landscape of deep networks. In this work, we aim to learn general post-hoc calibration functions that can preserve the top-k predictions of any deep network. We call this family of functions intra order-preserving functions. We propose a new neural network architecture that represents a class of intra order-preserving functions by combining common neural network components. Additionally, we introduce order-invariant and diagonal sub-families, which can act as regularization for better generalization when the training data size is small. We show the effectiveness of the proposed method across a wide range of datasets and classifiers. Our method outperforms state-of-the-art post-hoc calibration methods, namely temperature scaling and Dirichlet calibration, in multiple settings.

A Reduction from Reinforcement Learning to No-Regret Online Learning

We present a reduction from reinforcement learning (RL) to no-regret online learning based on the saddle-point formulation of RL, by which "any" online algorithm with sublinear regret can generate policies with provable performance guarantees. This new perspective decouples the RL problem into two parts: regret minimization and function approximation. The first part admits a standard online-learning analysis, and the second part can be quantified independently of the learning algorithm. Therefore, the proposed reduction can be used as a tool to systematically design new RL algorithms. We demonstrate this idea by devising a simple RL algorithm based on mirror descent and the generative-model oracle. For any $\gamma$-discounted tabular RL problem, with probability at least $1-\delta$, it learns an $\epsilon$-optimal policy using at most $\tilde{O}\left(\frac{|\mathcal{S}||\mathcal{A}|\log(\frac{1}{\delta})}{(1-\gamma)^4\epsilon^2}\right)$ samples. Furthermore, this algorithm admits a direct extension to linearly parameterized function approximators for large-scale applications, with computation and sample complexities independent of $|\mathcal{S}|$,$|\mathcal{A}|$, though at the cost of potential approximation bias.

Information Theoretic Model Predictive Q-Learning

Model-free Reinforcement Learning (RL) algorithms work well in sequential decision-making problems when experience can be collected cheaply and model-based RL is effective when system dynamics can be modeled accurately. However, both of these assumptions can be violated in real world problems such as robotics, where querying the system can be prohibitively expensive and real-world dynamics can be difficult to model accurately. Although sim-to-real approaches such as domain randomization attempt to mitigate the effects of biased simulation,they can still suffer from optimization challenges such as local minima and hand-designed distributions for randomization, making it difficult to learn an accurate global value function or policy that directly transfers to the real world. In contrast to RL, Model Predictive Control (MPC) algorithms use a simulator to optimize a simple policy class online, constructing a closed-loop controller that can effectively contend with real-world dynamics. MPC performance is usually limited by factors such as model bias and the limited horizon of optimization. In this work, we present a novel theoretical connection between information theoretic MPC and entropy regularized RL and develop a Q-learning algorithm that can leverage biased models. We validate the proposed algorithm on sim-to-sim control tasks to demonstrate the improvements over optimal control and reinforcement learning from scratch. Our approach paves the way for deploying reinforcement learning algorithms on real-robots in a systematic manner.

Continuous Online Learning and New Insights to Online Imitation Learning

Online learning is a powerful tool for analyzing iterative algorithms. However, the classic adversarial setup sometimes fails to capture certain regularity in online problems in practice. Motivated by this, we establish a new setup, called Continuous Online Learning (COL), where the gradient of online loss function changes continuously across rounds with respect to the learner's decisions. We show that COL covers and more appropriately describes many interesting applications, from general equilibrium problems (EPs) to optimization in episodic MDPs. Using this new setup, we revisit the difficulty of achieving sublinear dynamic regret. We prove that there is a fundamental equivalence between achieving sublinear dynamic regret in COL and solving certain EPs, and we present a reduction from dynamic regret to both static regret and convergence rate of the associated EP. At the end, we specialize these new insights into online imitation learning and show improved understanding of its learning stability.

Expressiveness and Learning of Hidden Quantum Markov Models

Extending classical probabilistic reasoning using the quantum mechanical view of probability has been of recent interest, particularly in the development of hidden quantum Markov models (HQMMs) to model stochastic processes. However, there has been little progress in characterizing the expressiveness of such models and learning them from data. We tackle these problems by showing that HQMMs are a special subclass of the general class of observable operator models (OOMs) that do not suffer from the \emph{negative probability problem} by design. We also provide a feasible retraction-based learning algorithm for HQMMs using constrained gradient descent on the Stiefel manifold of model parameters. We demonstrate that this approach is faster and scales to larger models than previous learning algorithms.

IRIS: Implicit Reinforcement without Interaction at Scale for Learning Control from Offline Robot Manipulation Data

Learning from offline task demonstrations is a problem of great interest in robotics. For simple short-horizon manipulation tasks with modest variation in task instances, offline learning from a small set of demonstrations can produce controllers that successfully solve the task. However, leveraging a fixed batch of data can be problematic for larger datasets and longer-horizon tasks with greater variations. The data can exhibit substantial diversity and consist of suboptimal solution approaches. In this paper, we propose Implicit Reinforcement without Interaction at Scale (IRIS), a novel framework for learning from large-scale demonstration datasets. IRIS factorizes the control problem into a goal-conditioned low-level controller that imitates short demonstration sequences and a high-level goal selection mechanism that sets goals for the low-level and selectively combines parts of suboptimal solutions leading to more successful task completions. We evaluate IRIS across three datasets, including the RoboTurk Cans dataset collected by humans via crowdsourcing, and show that performant policies can be learned from purely offline learning. Additional results and videos at https://stanfordvl.github.io/iris/ .