Existing online learning algorithms for adversarial Markov Decision Processes achieve ${O}(\sqrt{T})$ regret after $T$ rounds of interactions even if the loss functions are chosen arbitrarily by an adversary, with the caveat that the transition function has to be fixed. This is because it has been shown that adversarial transition functions make no-regret learning impossible. Despite such impossibility results, in this work, we develop algorithms that can handle both adversarial losses and adversarial transitions, with regret increasing smoothly in the degree of maliciousness of the adversary. More concretely, we first propose an algorithm that enjoys $\widetilde{{O}}(\sqrt{T} + C^{\textsf{P}})$ regret where $C^{\textsf{P}}$ measures how adversarial the transition functions are and can be at most ${O}(T)$. While this algorithm itself requires knowledge of $C^{\textsf{P}}$, we further develop a black-box reduction approach that removes this requirement. Moreover, we also show that further refinements of the algorithm not only maintains the same regret bound, but also simultaneously adapts to easier environments (where losses are generated in a certain stochastically constrained manner as in Jin et al. [2021]) and achieves $\widetilde{{O}}(U + \sqrt{UC^{\textsf{L}}} + C^{\textsf{P}})$ regret, where $U$ is some standard gap-dependent coefficient and $C^{\textsf{L}}$ is the amount of corruption on losses.

In online reinforcement learning (online RL), balancing exploration and exploitation is crucial for finding an optimal policy in a sample-efficient way. To achieve this, existing sample-efficient online RL algorithms typically consist of three components: estimation, planning, and exploration. However, in order to cope with general function approximators, most of them involve impractical algorithmic components to incentivize exploration, such as optimization within data-dependent level-sets or complicated sampling procedures. To address this challenge, we propose an easy-to-implement RL framework called \textit{Maximize to Explore} (\texttt{MEX}), which only needs to optimize \emph{unconstrainedly} a single objective that integrates the estimation and planning components while balancing exploration and exploitation automatically. Theoretically, we prove that \texttt{MEX} achieves a sublinear regret with general function approximations for Markov decision processes (MDP) and is further extendable to two-player zero-sum Markov games (MG). Meanwhile, we adapt deep RL baselines to design practical versions of \texttt{MEX}, in both model-free and model-based manners, which can outperform baselines by a stable margin in various MuJoCo environments with sparse rewards. Compared with existing sample-efficient online RL algorithms with general function approximations, \texttt{MEX} achieves similar sample efficiency while enjoying a lower computational cost and is more compatible with modern deep RL methods.

Ill-posed linear inverse problems arise frequently in various applications, from computational photography to medical imaging. A recent line of research exploits Bayesian inference with informative priors to handle the ill-posedness of such problems. Amongst such priors, score-based generative models (SGM) have recently been successfully applied to several different inverse problems. In this study, we exploit the particular structure of the prior defined by the SGM to define a sequence of intermediate linear inverse problems. As the noise level decreases, the posteriors of these inverse problems get closer to the target posterior of the original inverse problem. To sample from this sequence of posteriors, we propose the use of Sequential Monte Carlo (SMC) methods. The proposed algorithm, MCGDiff, is shown to be theoretically grounded and we provide numerical simulations showing that it outperforms competing baselines when dealing with ill-posed inverse problems in a Bayesian setting.

A Bayesian coreset is a small, weighted subset of data that replaces the full dataset during inference in order to reduce computational cost. However, state of the art methods for tuning coreset weights are expensive, require nontrivial user input, and impose constraints on the model. In this work, we propose a new method -- Coreset MCMC -- that simulates a Markov chain targeting the coreset posterior, while simultaneously updating the coreset weights using those same draws. Coreset MCMC is simple to implement and tune, and can be used with any existing MCMC kernel. We analyze Coreset MCMC in a representative setting to obtain key insights about the convergence behaviour of the method. Empirical results demonstrate that Coreset MCMC provides higher quality posterior approximations and reduced computational cost compared with other coreset construction methods. Further, compared with other general subsampling MCMC methods, we find that Coreset MCMC has a higher sampling efficiency with competitively accurate posterior approximations.

Reinforcement Learning (RL) is notoriously data-inefficient, which makes training on a real robot difficult. While model-based RL algorithms (world models) improve data-efficiency to some extent, they still require hours or days of interaction to learn skills. Recently, offline RL has been proposed as a framework for training RL policies on pre-existing datasets without any online interaction. However, constraining an algorithm to a fixed dataset induces a state-action distribution shift between training and inference, and limits its applicability to new tasks. In this work, we seek to get the best of both worlds: we consider the problem of pretraining a world model with offline data collected on a real robot, and then finetuning the model on online data collected by planning with the learned model. To mitigate extrapolation errors during online interaction, we propose to regularize the planner at test-time by balancing estimated returns and (epistemic) model uncertainty. We evaluate our method on a variety of visuo-motor control tasks in simulation and on a real robot, and find that our method enables few-shot finetuning to seen and unseen tasks even when offline data is limited. Videos, code, and data are available at https://yunhaifeng.com/FOWM .

Data-driven models for nonlinear dynamical systems based on approximating the underlying Koopman operator or generator have proven to be successful tools for forecasting, feature learning, state estimation, and control. It has become well known that the Koopman generators for control-affine systems also have affine dependence on the input, leading to convenient finite-dimensional bilinear approximations of the dynamics. Yet there are still two main obstacles that limit the scope of current approaches for approximating the Koopman generators of systems with actuation. First, the performance of existing methods depends heavily on the choice of basis functions over which the Koopman generator is to be approximated; and there is currently no universal way to choose them for systems that are not measure preserving. Secondly, if we do not observe the full state, then it becomes necessary to account for the dependence of the output time series on the sequence of supplied inputs when constructing observables to approximate Koopman operators. To address these issues, we write the dynamics of observables governed by the Koopman generator as a bilinear hidden Markov model, and determine the model parameters using the expectation-maximization (EM) algorithm. The E-step involves a standard Kalman filter and smoother, while the M-step resembles control-affine dynamic mode decomposition for the generator. We demonstrate the performance of this method on three examples, including recovery of a finite-dimensional Koopman-invariant subspace for an actuated system with a slow manifold; estimation of Koopman eigenfunctions for the unforced Duffing equation; and model-predictive control of a fluidic pinball system based only on noisy observations of lift and drag.

The Option Keyboard (OK) was recently proposed as a method for transferring behavioral knowledge across tasks. OK transfers knowledge by adaptively combining subsets of known behaviors using Successor Features (SFs) and Generalized Policy Improvement (GPI). However, it relies on hand-designed state-features and task encodings which are cumbersome to design for every new environment. In this work, we propose the "Successor Features Keyboard" (SFK), which enables transfer with discovered state-features and task encodings. To enable discovery, we propose the "Categorical Successor Feature Approximator" (CSFA), a novel learning algorithm for estimating SFs while jointly discovering state-features and task encodings. With SFK and CSFA, we achieve the first demonstration of transfer with SFs in a challenging 3D environment where all the necessary representations are discovered. We first compare CSFA against other methods for approximating SFs and show that only CSFA discovers representations compatible with SF&GPI at this scale. We then compare SFK against transfer learning baselines and show that it transfers most quickly to long-horizon tasks.

Agile and adaptive maneuvers such as fall recovery, high-speed turning, and sprinting in the wild are challenging for legged systems. We propose a Curricular Hindsight Reinforcement Learning (CHRL) that learns an end-to-end tracking controller that achieves powerful agility and adaptation for the legged robot. The two key components are (I) a novel automatic curriculum strategy on task difficulty and (ii) a Hindsight Experience Replay strategy adapted to legged locomotion tasks. We demonstrated successful agile and adaptive locomotion on a real quadruped robot that performed fall recovery autonomously, coherent trotting, sustained outdoor speeds up to 3.45 m/s, and tuning speeds up to 3.2 rad/s. This system produces adaptive behaviours responding to changing situations and unexpected disturbances on natural terrains like grass and dirt.

A topic of great current interest is Causal Representation Learning (CRL), whose goal is to learn a causal model for hidden features in a data-driven manner. Unfortunately, CRL is severely ill-posed since it is a combination of the two notoriously ill-posed problems of representation learning and causal discovery. Yet, finding practical identifiability conditions that guarantee a unique solution is crucial for its practical applicability. Most approaches so far have been based on assumptions on the latent causal mechanisms, such as temporal causality, or existence of supervision or interventions; these can be too restrictive in actual applications. Here, we show identifiability based on novel, weak constraints, which requires no temporal structure, intervention, nor weak supervision. The approach is based assuming the observational mixing exhibits a suitable grouping of the observational variables. We also propose a novel self-supervised estimation framework consistent with the model, prove its statistical consistency, and experimentally show its superior CRL performances compared to the state-of-the-art baselines. We further demonstrate its robustness against latent confounders and causal cycles.

The core principle of Variational Inference (VI) is to convert the statistical inference problem of computing complex posterior probability densities into a tractable optimization problem. This property enables VI to be faster than several sampling-based techniques. However, the traditional VI algorithm is not scalable to large data sets and is unable to readily infer out-of-bounds data points without re-running the optimization process. Recent developments in the field, like stochastic-, black box-, and amortized-VI, have helped address these issues. Generative modeling tasks nowadays widely make use of amortized VI for its efficiency and scalability, as it utilizes a parameterized function to learn the approximate posterior density parameters. In this paper, we review the mathematical foundations of various VI techniques to form the basis for understanding amortized VI. Additionally, we provide an overview of the recent trends that address several issues of amortized VI, such as the amortization gap, generalization issues, inconsistent representation learning, and posterior collapse. Finally, we analyze alternate divergence measures that improve VI optimization.