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In this paper, we study the problem of methodically obtaining a sufficient set of kinesthetic demonstrations, one at a time, such that a robot can be confident of its ability to perform a complex manipulation task in a given region of its workspace. Although Learning from Demonstrations has been an active area of research, the problems of checking whether a set of demonstrations is sufficient, and systematically seeking additional demonstrations have remained open. We present a novel approach to address these open problems using (i) a screw geometric representation to generate manipulation plans from demonstrations, which makes the sufficiency of a set of demonstrations measurable; (ii) a sampling strategy based on PAC-learning from multi-armed bandit optimization to evaluate the robot's ability to generate manipulation plans in a subregion of its task space; and (iii) a heuristic to seek additional demonstration from areas of weakness. Thus, we present an approach for the robot to incrementally and actively ask for new demonstration examples until the robot can assess with high confidence that it can perform the task successfully. We present experimental results on two example manipulation tasks, namely, pouring and scooping, to illustrate our approach. A short video on the method: https://youtu.be/R-qICICdEos, Comment: 8 pages, 6 figures, under review in IEEE Robotics and Automation Letters

Fully optimized automation of behavioral training protocols for lab animals like rodents has long been a coveted goal for researchers. It is an otherwise labor-intensive and time-consuming process that demands close interaction between the animal and the researcher. In this work, we used a data-driven approach to optimize the way rodents are trained in labs. In pursuit of our goal, we looked at data augmentation, a technique that scales well in data-poor environments. Using data augmentation, we built several artificial rodent models, which in turn would be used to build an efficient and automatic trainer. Then we developed a novel similarity metric based on the action probability distribution to measure the behavioral resemblance of our models to that of real rodents., Comment: 5 pages, 3 figures

Determining the spectrum and wave functions of excited states of a system is crucial in quantum physics and chemistry. Low-depth quantum algorithms, such as the Variational Quantum Eigensolver (VQE) and its variants, can be used to determine the ground-state energy. However, current approaches to computing excited states require numerous controlled unitaries, making the application of the original Variational Quantum Deflation (VQD) algorithm to problems in chemistry or physics suboptimal. In this study, we introduce a charge-preserving VQD (CPVQD) algorithm, designed to incorporate symmetry and the corresponding conserved charge into the VQD framework. This results in dimension reduction, significantly enhancing the efficiency of excited-state computations. We present benchmark results with GPU-accelerated simulations using systems up to 24 qubits, showcasing applications in high-energy physics, nuclear physics, and quantum chemistry. This work is performed on NERSC's Perlmutter system using NVIDIA's open-source platform for accelerated quantum supercomputing - CUDA-Q., Comment: 20 pages, 6 figures, 1 table

Present quantum computers are constrained by limited qubit capacity and restricted physical connectivity, leading to challenges in large-scale quantum computations. Distributing quantum computations across a network of quantum computers is a promising way to circumvent these challenges and facilitate large quantum computations. However, distributed quantum computations require entanglements (to execute remote gates) which can incur significant generation latency and, thus, lead to decoherence of qubits. In this work, we consider the problem of distributing quantum circuits across a quantum network to minimize the execution time. The problem entails mapping the circuit qubits to network memories, including within each computer since limited connectivity within computers can affect the circuit execution time. We provide two-step solutions for the above problem: In the first step, we allocate qubits to memories to minimize the estimated execution time; for this step, we design an efficient algorithm based on an approximation algorithm for the max-quadratic-assignment problem. In the second step, we determine an efficient execution scheme, including generating required entanglements with minimum latency under the network resource and decoherence constraints; for this step, we develop two algorithms with appropriate performance guarantees under certain settings or assumptions. We consider multiple protocols for executing remote gates, viz., telegates and cat-entanglements. With extensive simulations over NetSquid, a quantum network simulator, we demonstrate the effectiveness of our developed techniques and show that they outperform a scheme based on prior work by up to 95%.

Building large-scale quantum computers, essential to demonstrating quantum advantage, is a key challenge. Quantum Networks (QNs) can help address this challenge by enabling the construction of large, robust, and more capable quantum computing platforms by connecting smaller quantum computers. Moreover, unlike classical systems, QNs can enable fully secured long-distance communication. Thus, quantum networks lie at the heart of the success of future quantum information technologies. In quantum networks, multipartite entangled states distributed over the network help implement and support many quantum network applications for communications, sensing, and computing. Our work focuses on developing optimal techniques to generate and distribute multipartite entanglement states efficiently. Prior works on generating general multipartite entanglement states have focused on the objective of minimizing the number of maximally entangled pairs (EPs) while ignoring the heterogeneity of the network nodes and links as well as the stochastic nature of underlying processes. In this work, we develop a hypergraph based linear programming framework that delivers optimal (under certain assumptions) generation schemes for general multipartite entanglement represented by graph states, under the network resources, decoherence, and fidelity constraints, while considering the stochasticity of the underlying processes. We illustrate our technique by developing generation schemes for the special cases of path and tree graph states, and discuss optimized generation schemes for more general classes of graph states. Using extensive simulations over a quantum network simulator (NetSquid), we demonstrate the effectiveness of our developed techniques and show that they outperform prior known schemes by up to orders of magnitude., Comment: 11 pages, 13 figures

Near-term quantum computers can hold only a small number of qubits. One way to facilitate large-scale quantum computations is through a distributed network of quantum computers. In this work, we consider the problem of distributing quantum programs represented as quantum circuits across a quantum network of heterogeneous quantum computers, in a way that minimizes the overall communication cost required to execute the distributed circuit. We consider two ways of communicating: cat-entanglement that creates linked copies of qubits across pairs of computers, and teleportation. The heterogeneous computers impose constraints on cat-entanglement and teleportation operations that can be chosen by an algorithm. We first focus on a special case that only allows cat-entanglements and not teleportations for communication. We provide a two-step heuristic for solving this specialized setting: (i) finding an assignment of qubits to computers using Tabu search, and (ii) using an iterative greedy algorithm designed for a constrained version of the set cover problem to determine cat-entanglement operations required to execute gates locally. For the general case, which allows both forms of communication, we propose two algorithms that subdivide the quantum circuit into several portions and apply the heuristic for the specialized setting on each portion. Teleportations are then used to stitch together the solutions for each portion. Finally, we simulate our algorithms on a wide range of randomly generated quantum networks and circuits, and study the properties of their results with respect to several varying parameters.

Quantum network communication is challenging, as the No-Cloning theorem in quantum regime makes many classical techniques inapplicable. For long-distance communication, the only viable approach is teleportation of quantum states, which requires a prior distribution of entangled pairs (EPs) of qubits. Establishment of EPs across remote nodes can incur significant latency due to the low probability of success of the underlying physical processes. To reduce EP generation latency, prior works have looked at selection of efficient entanglement-routing paths and simultaneous use of multiple such paths for EP generation. In this paper, we propose and investigate a complementary technique to reduce EP generation latency--to pre-distribute EPs over certain (pre-determined) pairs of network nodes; these pre-distributed EPs can then be used to generate EPs for the requested pairs, when needed, with lower generation latency. For such an pre-distribution approach to be most effective, we need to address an optimization problem of selection of node-pairs where the EPs should be pre-distributed to minimize the generation latency of expected EP requests, under a given cost constraint. In this paper, we appropriately formulate the above optimization problem and design two efficient algorithms, one of which is a greedy approach based on an approximation algorithm for a special case. Via extensive evaluations over the NetSquid simulator, we demonstrate the effectiveness of our approach and developed techniques; we show that our developed algorithms outperform a naive approach by up to an order of magnitude., Comment: 11 pages, 9 figures

Quantum network communication is challenging, as the No-cloning theorem in quantum regime makes many classical techniques inapplicable. For long-distance communication, the only viable communication approach is teleportation of quantum states, which requires a prior distribution of entangled pairs (EPs) of qubits. Establishment of EPs across remote nodes can incur significant latency due to the low probability of success of the underlying physical processes. The focus of our work is to develop efficient techniques that minimize EP generation latency. Prior works have focused on selecting entanglement paths; in contrast, we select entanglement swapping trees--a more accurate representation of the entanglement generation structure. We develop a dynamic programming algorithm to select an optimal swapping-tree for a single pair of nodes, under the given capacity and fidelity constraints. For the general setting, we develop an efficient iterative algorithm to compute a set of swapping trees. We present simulation results which show that our solutions outperform the prior approaches by an order of magnitude and are viable for long-distance entanglement generation.

In medical decision making, we have to choose among several expensive diagnostic tests such that the certainty about a patient's health is maximized while remaining within the bounds of resources like time and money. The expected increase in certainty in the patient's condition due to performing a test is called the value of information (VoI) for that test. In general, VoI relates to acquiring additional information to improve decision-making based on probabilistic reasoning in an uncertain system. This paper presents a framework for acquiring information based on VoI in uncertain systems modeled as Probabilistic Logic Programs (PLPs). Optimal decision-making in uncertain systems modeled as PLPs have already been studied before. But, acquiring additional information to further improve the results of making the optimal decision has remained open in this context. We model decision-making in an uncertain system with a PLP and a set of top-level queries, with a set of utility measures over the distributions of these queries. The PLP is annotated with a set of atoms labeled as "observable"; in the medical diagnosis example, the observable atoms will be results of diagnostic tests. Each observable atom has an associated cost. This setting of optimally selecting observations based on VoI is more general than that considered by any prior work. Given a limited budget, optimally choosing observable atoms based on VoI is intractable in general. We give a greedy algorithm for constructing a "conditional plan" of observations: a schedule where the selection of what atom to observe next depends on earlier observations. We show that, preempting the algorithm anytime before completion provides a usable result, the result improves over time, and, in the absence of a well-defined budget, converges to the optimal solution., Comment: In Proceedings ICLP 2019, arXiv:1909.07646

Probabilistic Logic Programs (PLPs) generalize traditional logic programs and allow the encoding of models combining logical structure and uncertainty. In PLP, inference is performed by summarizing the possible worlds which entail the query in a suitable data structure, and using it to compute the answer probability. Systems such as ProbLog, PITA, etc., use propositional data structures like explanation graphs, BDDs, SDDs, etc., to represent the possible worlds. While this approach saves inference time due to substructure sharing, there are a number of problems where a more compact data structure is possible. We propose a data structure called Ordered Symbolic Derivation Diagram (OSDD) which captures the possible worlds by means of constraint formulas. We describe a program transformation technique to construct OSDDs via query evaluation, and give procedures to perform exact and approximate inference over OSDDs. Our approach has two key properties. Firstly, the exact inference procedure is a generalization of traditional inference, and results in speedup over the latter in certain settings. Secondly, the approximate technique is a generalization of likelihood weighting in Bayesian Networks, and allows us to perform sampling-based inference with lower rejection rate and variance. We evaluate the effectiveness of the proposed techniques through experiments on several problems. This paper is under consideration for acceptance in TPLP., Comment: Paper presented at the 34nd International Conference on Logic Programming (ICLP 2018), Oxford, UK, July 14 to July 17, 2018 18 pages, LaTeX, 5 PDF figures (arXiv:YYMM.NNNNN)

In this paper, we consider the problem of lifted inference in the context of Prism-like probabilistic logic programming languages. Traditional inference in such languages involves the construction of an explanation graph for the query and computing probabilities over this graph. When evaluating queries over probabilistic logic programs with a large number of instances of random variables, traditional methods treat each instance separately. For many programs and queries, we observe that explanations can be summarized into substantially more compact structures, which we call lifted explanation graphs. In this paper, we define lifted explanation graphs and operations over them. In contrast to existing lifted inference techniques, our method for constructing lifted explanations naturally generalizes existing methods for constructing explanation graphs. To compute probability of query answers, we solve recurrences generated from the lifted graphs. We show examples where the use of our technique reduces the asymptotic complexity of inference.

Generalized Probabilistic Logic (GPL) is a temporal logic, based on the modal mu-calculus, for specifying properties of reactive probabilistic systems. We explore XPL, an extension to GPL allowing the semantics of nondeterminism present in Markov decision processes (MDPs). XPL is expressive enough that a number of independently studied problems--- such as termination of Recursive MDPs (RMDPs), PCTL* model checking of MDPs, and reachability for Branching MDPs--- can all be cast as model checking over XPL. Termination of multi-exit RMDPs is undecidable; thus, model checking in XPL is undecidable in general. We define a subclass, called separable XPL, for which model checking is decidable. Decidable problems such as termination of 1-exit RMDPs, PCTL* model checking of MDPs, and reachability for Branching MDPs can be reduced to model checking separable XPL. Thus, XPL forms a uniform framework for studying problems involving systems with non-deterministic and probabilistic behaviors, while separable XPL provides a way to solve decidable fragments of these problems.

Probabilistic Logic Programming (PLP) languages enable programmers to specify systems that combine logical models with statistical knowledge. The inference problem, to determine the probability of query answers in PLP, is intractable in general, thereby motivating the need for approximate techniques. In this paper, we present a technique for approximate inference of conditional probabilities for PLP queries. It is an Adaptive Markov Chain Monte Carlo (MCMC) technique, where the distribution from which samples are drawn is modified as the Markov Chain is explored. In particular, the distribution is progressively modified to increase the likelihood that a generated sample is consistent with evidence. In our context, each sample is uniquely characterized by the outcomes of a set of random variables. Inspired by reinforcement learning, our technique propagates rewards to random variable/outcome pairs used in a sample based on whether the sample was consistent or not. The cumulative rewards of each outcome is used to derive a new "adapted distribution" for each random variable. For a sequence of samples, the distributions are progressively adapted after each sample. For a query with "Markovian evaluation structure", we show that the adapted distribution of samples converges to the query's conditional probability distribution. For Markovian queries, we present a modified adaptation process that can be used in adaptive MCMC as well as adaptive independent sampling. We empirically evaluate the effectiveness of the adaptive sampling methods for queries with and without Markovian evaluation structure.

We present a formulation of the problem of probabilistic model checking as one of query evaluation over probabilistic logic programs. To the best of our knowledge, our formulation is the first of its kind, and it covers a rich class of probabilistic models and probabilistic temporal logics. The inference algorithms of existing probabilistic logic-programming systems are well defined only for queries with a finite number of explanations. This restriction prohibits the encoding of probabilistic model checkers, where explanations correspond to executions of the system being model checked. To overcome this restriction, we propose a more general inference algorithm that uses finite generative structures (similar to automata) to represent families of explanations. The inference algorithm computes the probability of a possibly infinite set of explanations directly from the finite generative structure. We have implemented our inference algorithm in XSB Prolog, and use this implementation to encode probabilistic model checkers for a variety of temporal logics, including PCTL and GPL (which subsumes PCTL*). Our experiment results show that, despite the highly declarative nature of their encodings, the model checkers constructed in this manner are competitive with their native implementations.

Probabilistic Logic Programming (PLP), exemplified by Sato and Kameya's PRISM, Poole's ICL, De Raedt et al's ProbLog and Vennekens et al's LPAD, combines statistical and logical knowledge representation and inference. Inference in these languages is based on enumerative construction of proofs over logic programs. Consequently, these languages permit very limited use of random variables with continuous distributions. In this paper, we extend PRISM with Gaussian random variables and linear equality constraints, and consider the problem of parameter learning in the extended language. Many statistical models such as finite mixture models and Kalman filter can be encoded in extended PRISM. Our EM-based learning algorithm uses a symbolic inference procedure that represents sets of derivations without enumeration. This permits us to learn the distribution parameters of extended PRISM programs with discrete as well as Gaussian variables. The learning algorithm naturally generalizes the ones used for PRISM and Hybrid Bayesian Networks., Comment: 7 pages. Main contribution: Learning algorithm. Inference appears in http://arxiv.org/abs/1112.2681

Probabilistic Logic Programming (PLP), exemplified by Sato and Kameya's PRISM, Poole's ICL, Raedt et al's ProbLog and Vennekens et al's LPAD, is aimed at combining statistical and logical knowledge representation and inference. A key characteristic of PLP frameworks is that they are conservative extensions to non-probabilistic logic programs which have been widely used for knowledge representation. PLP frameworks extend traditional logic programming semantics to a distribution semantics, where the semantics of a probabilistic logic program is given in terms of a distribution over possible models of the program. However, the inference techniques used in these works rely on enumerating sets of explanations for a query answer. Consequently, these languages permit very limited use of random variables with continuous distributions. In this paper, we present a symbolic inference procedure that uses constraints and represents sets of explanations without enumeration. This permits us to reason over PLPs with Gaussian or Gamma-distributed random variables (in addition to discrete-valued random variables) and linear equality constraints over reals. We develop the inference procedure in the context of PRISM; however the procedure's core ideas can be easily applied to other PLP languages as well. An interesting aspect of our inference procedure is that PRISM's query evaluation process becomes a special case in the absence of any continuous random variables in the program. The symbolic inference procedure enables us to reason over complex probabilistic models such as Kalman filters and a large subclass of Hybrid Bayesian networks that were hitherto not possible in PLP frameworks. (To appear in Theory and Practice of Logic Programming)., Comment: 12 pages. arXiv admin note: substantial text overlap with arXiv:1203.4287