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1. Exploratory Grasping: Asymptotically Optimal Algorithms for Grasping Challenging Polyhedral Objects

   Danielczuk, Michael ; Balakrishna, Ashwin ; Brown, Daniel ; Devgon, Shivin ; Goldberg, Ken ( January 2020 , 4th Conference on Robot Learning)

   There has been significant recent work on data-driven algorithms for learning general-purpose grasping policies. However, these policies can consis- tently fail to grasp challenging objects which are significantly out of the distribution of objects in the training data or which have very few high quality grasps. Moti- vated by such objects, we propose a novel problem setting, Exploratory Grasping, for efficiently discovering reliable grasps on an unknown polyhedral object via sequential grasping, releasing, and toppling. We formalize Exploratory Grasping as a Markov Decision Process where we assume that the robot can (1) distinguish stable poses of a polyhedral object of unknown geometry, (2) generate grasp can- didates on these poses and execute them, (3) determine whether each grasp is successful, and (4) release the object into a random new pose after a grasp success or topple the object after a grasp failure. We study the theoretical complexity of Exploratory Grasping in the context of reinforcement learning and present an efficient bandit-style algorithm, Bandits for Online Rapid Grasp Exploration Strategy (BORGES), which leverages the structure of the problem to efficiently discover high performing grasps for each object stable pose. BORGES can be used to complement any general-purpose grasping algorithm with any grasp modality (parallel-jaw, suction, multi-fingered, etc) to learn policies for objects in which they exhibit persistent failures. Simulation experiments suggest that BORGES can significantly outperform both general-purpose grasping pipelines and two other online learning algorithms and achieves performance within 5% of the optimal policy within 1000 and 8000 timesteps on average across 46 challenging objects from the Dex-Net adversarial and EGAD! object datasets, respectively. Initial physical experiments suggest that BORGES can improve grasp success rate by 45% over a Dex-Net baseline with just 200 grasp attempts in the real world. See https://tinyurl.com/exp-grasping for supplementary material and videos. 

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2. Recovering Structured Probability Matrices.

   https://doi.org/10.4230/LIPIcs.ITCS.2018.46  

   Huang, Qingqing ; Kakade, Sham M. ; Kong, Weihao ; Valiant, Gregory ( May 2018 , 9th Innovations in Theoretical Computer Science Conference (ITCS 2018))

   We consider the problem of accurately recovering a matrix B of size M by M, which represents a probability distribution over M^2 outcomes, given access to an observed matrix of "counts" generated by taking independent samples from the distribution B. How can structural properties of the underlying matrix B be leveraged to yield computationally efficient and information theoretically optimal reconstruction algorithms? When can accurate reconstruction be accomplished in the sparse data regime? This basic problem lies at the core of a number of questions that are currently being considered by different communities, including building recommendation systems and collaborative filtering in the sparse data regime, community detection in sparse random graphs, learning structured models such as topic models or hidden Markov models, and the efforts from the natural language processing community to compute "word embeddings". Many aspects of this problem---both in terms of learning and property testing/estimation and on both the algorithmic and information theoretic sides---remain open. Our results apply to the setting where B has a low rank structure. For this setting, we propose an efficient (and practically viable) algorithm that accurately recovers the underlying M by M matrix using O(M) samples} (where we assume the rank is a constant). This linear sample complexity is optimal, up to constant factors, in an extremely strong sense: even testing basic properties of the underlying matrix (such as whether it has rank 1 or 2) requires Omega(M) samples. Additionally, we provide an even stronger lower bound showing that distinguishing whether a sequence of observations were drawn from the uniform distribution over M observations versus being generated by a well-conditioned Hidden Markov Model with two hidden states requires Omega(M) observations, while our positive results for recovering B immediately imply that Omega(M) observations suffice to learn such an HMM. This lower bound precludes sublinear-sample hypothesis tests for basic properties, such as identity or uniformity, as well as sublinear sample estimators for quantities such as the entropy rate of HMMs. 

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3. Robust learning under clean-label attack

   Blum, A. ; Hanneke, S. ; Qian, J. ; Shao, H. ( January 2021 , Conference on Learning Theory)

   Belkin, M. ; Kpotufe, S. (Ed.)

   We study the problem of robust learning under clean-label data-poisoning attacks, where the at-tacker injects (an arbitrary set of) correctly-labeled examples to the training set to fool the algorithm into making mistakes on specific test instances at test time. The learning goal is to minimize the attackable rate (the probability mass of attackable test instances), which is more difficult than optimal PAC learning. As we show, any robust algorithm with diminishing attackable rate can achieve the optimal dependence on ε in its PAC sample complexity, i.e., O(1/ε). On the other hand, the attackable rate might be large even for some optimal PAC learners, e.g., SVM for linear classifiers. Furthermore, we show that the class of linear hypotheses is not robustly learnable when the data distribution has zero margin and is robustly learnable in the case of positive margin but requires sample complexity exponential in the dimension. For a general hypothesis class with bounded VC dimension, if the attacker is limited to add at most t >0 poison examples, the optimal robust learning sample complexity grows almost linearly with t. 

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4. Adaptive Quantum Simulated Annealing for Bayesian Inference and Estimating Partition Functions

   Harrow, Aram W. ; Wei, AY ( January 2020 , Proceedings of the 2020 ACM-SIAM Symposium on Discrete Algorithms)

   Markov chain Monte Carlo algorithms have important applications in counting problems and in machine learning problems, settings that involve estimating quantities that are difficult to compute exactly. How much can quantum computers speed up classical Markov chain algorithms? In this work we consider the problem of speeding up simulated annealing algorithms, where the stationary distributions of the Markov chains are Gibbs distributions at temperatures specified according to an annealing schedule. We construct a quantum algorithm that both adaptively constructs an annealing schedule and quantum samples at each temperature. Our adaptive annealing schedule roughly matches the length of the best classical adaptive annealing schedules and improves on nonadaptive temperature schedules by roughly a quadratic factor. Our dependence on the Markov chain gap matches other quantum algorithms and is quadratically better than what classical Markov chains achieve. Our algorithm is the first to combine both of these quadratic improvements. Like other quantum walk algorithms, it also improves on classical algorithms by producing “qsamples” instead of classical samples. This means preparing quantum states whose amplitudes are the square roots of the target probability distribution. In constructing the annealing schedule we make use of amplitude estimation, and we introduce a method for making amplitude estimation nondestructive at almost no additional cost, a result that may have independent interest. Finally we demonstrate how this quantum simulated annealing algorithm can be applied to the problems of estimating partition functions and Bayesian inference. 

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5. Distributionally Robust Q-Learning

   Liu, Zijian ; Bai, Qinxun ; Blanchet, Jose H. ; Dong, Perry ; Xu, Wei ; Zhou, Zhengqing ; Zhou, Zhengyuan ( July 2022 , Proceedings of Machine Learning Research)

   Chaudhuri, Kamalika ; Jegelka, Stefanie ; Song, Le ; Szepesvari, Csaba ; Niu, Gang ; Sabato, Sivan (Ed.)

   Reinforcement learning (RL) has demonstrated remarkable achievements in simulated environments. However, carrying this success to real environments requires the important attribute of robustness, which the existing RL algorithms often lack as they assume that the future deployment environment is the same as the training environment (i.e. simulator) in which the policy is learned. This assumption often does not hold due to the discrepancy between the simulator and the real environment and, as a result, and hence renders the learned policy fragile when deployed. In this paper, we propose a novel distributionally robust Q-learning algorithm that learns the best policy in the worst distributional perturbation of the environment. Our algorithm first transforms the infinite-dimensional learning problem (since the environment MDP perturbation lies in an infinite-dimensional space) into a finite-dimensional dual problem and subsequently uses a multi-level Monte-Carlo scheme to approximate the dual value using samples from the simulator. Despite the complexity, we show that the resulting distributionally robust Q-learning algorithm asymptotically converges to optimal worst-case policy, thus making it robust to future environment changes. Simulation results further demonstrate its strong empirical robustness. 

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