We study the symmetric weighted first-order model counting task and present ApproxWFOMC, a novel anytime method for efficiently bounding the weighted first-order model count in the presence of an unweighted first-order model counting oracle. The algorithm has applications to inference in a variety of first-order probabilistic representations, such as Markov logic networks and probabilistic logic programs. Crucially for many applications, we make no assumptions on the form of the input sentence. Instead, our algorithm makes use of the symmetry inherent in the problem by imposing cardinality constraints on the number of possible true groundings of a sentence's literals. Realising the first-order model counting oracle in practice using the approximate hashing-based model counter ApproxMC3, we show how our algorithm outperforms existing approximate and exact techniques for inference in first-order probabilistic models. We additionally provide PAC guarantees on the generated bounds.

The recent usage of technical systems in human-centric environments leads to the question, how to teach technical systems, e.g., robots, to understand, learn, and perform tasks desired by the human. Therefore, an accurate representation of knowledge is essential for the system to work as expected. This article mainly gives insight into different knowledge representation techniques and their categorization into various problem domains in artificial intelligence. Additionally, applications of presented knowledge representations are introduced in everyday robotics tasks. By means of the provided taxonomy, the search for a proper knowledge representation technique regarding a specific problem should be facilitated.

This letter proposes a novel reinforcement learning method for the synthesis of a control policy satisfying a control specification described by a linear temporal logic formula. We assume that the controlled system is modeled by a Markov decision process (MDP). We transform the specification to a limit-deterministic B\"uchi automaton (LDBA) with several accepting sets that accepts all infinite sequences satisfying the formula. The LDBA is augmented so that it explicitly records the previous visits to accepting sets. We take a product of the augmented LDBA and the MDP, based on which we define a reward function. The agent gets rewards whenever state transitions are in an accepting set that has not been visited for a certain number of steps. Consequently, sparsity of rewards is relaxed and optimal circulations among the accepting sets are learned. We show that the proposed method can learn an optimal policy when the discount factor is sufficiently close to one.

In order to collaborate safely and efficiently, robots need to anticipate how their human partners will behave. Some of today's robots model humans as if they were also robots, and assume users are always optimal. Other robots account for human limitations, and relax this assumption so that the human is noisily rational. Both of these models make sense when the human receives deterministic rewards: i.e., gaining either $100 or $130 with certainty. But in real world scenarios, rewards are rarely deterministic. Instead, we must make choices subject to risk and uncertainty--and in these settings, humans exhibit a cognitive bias towards suboptimal behavior. For example, when deciding between gaining $100 with certainty or $130 only 80% of the time, people tend to make the risk-averse choice--even though it leads to a lower expected gain! In this paper, we adopt a well-known Risk-Aware human model from behavioral economics called Cumulative Prospect Theory and enable robots to leverage this model during human-robot interaction (HRI). In our user studies, we offer supporting evidence that the Risk-Aware model more accurately predicts suboptimal human behavior. We find that this increased modeling accuracy results in safer and more efficient human-robot collaboration. Overall, we extend existing rational human models so that collaborative robots can anticipate and plan around suboptimal human behavior during HRI.

Recent research in behaviour understanding through language grounding has shown it is possible to automatically generate behaviour models from textual instructions. These models usually have goal-oriented structure and are modelled with different formalisms from the planning domain such as the Planning Domain Definition Language. One major problem that still remains is that there are no benchmark datasets for comparing the different model generation approaches, as each approach is usually evaluated on domain-specific application. To allow the objective comparison of different methods for model generation from textual instructions, in this report we introduce a dataset consisting of 83 textual instructions in English language, their refinement in a more structured form as well as manually developed plans for each of the instructions. The dataset is publicly available to the community.

Many medical decision-making settings can be framed as partially observed Markov decision processes (POMDPs). However, popular two-stage approaches that first learn a POMDP model and then solve it often fail because the model that best fits the data may not be the best model for planning. We introduce a new optimization objective that (a) produces both high-performing policies and high-quality generative models, even when some observations are irrelevant for planning, and (b) does so in the kinds of batch, off-policy settings common in medicine. We demonstrate our approach on synthetic examples and a real-world hypotension management task.

Autonomous systems are often required to operate in partially observable environments. They must reliably execute a specified objective even with incomplete information about the state of the environment. We propose a methodology to synthesize policies that satisfy a linear temporal logic formula in a partially observable Markov decision process (POMDP). By formulating a planning problem, we show how to use point-based value iteration methods to efficiently approximate the maximum probability of satisfying a desired logical formula and compute the associated belief state policy. We demonstrate that our method scales to large POMDP domains and provides strong bounds on the performance of the resulting policy.

We consider the problem of discriminatively learning restricted Boltzmann machines in the presence of relational data. Unlike previous approaches that employ a rule learner (for structure learning) and a weight learner (for parameter learning) sequentially, we develop a gradient-boosted approach that performs both simultaneously. Our approach learns a set of weak relational regression trees, whose paths from root to leaf are conjunctive clauses and represent the structure, and whose leaf values represent the parameters. When the learned relational regression trees are transformed into a lifted RBM, its hidden nodes are precisely the conjunctive clauses derived from the relational regression trees. This leads to a more interpretable and explainable model. Our empirical evaluations clearly demonstrate this aspect, while displaying no loss in effectiveness of the learned models.

We present several new results on the feasibility of inferring the hidden states in strongly-connected trackable weak models. Here, a weak model is a directed graph in which each node is assigned a set of colors which may be emitted when that node is visited. A hypothesis is a node sequence which is consistent with a given color sequence. A weak model is said to be trackable if the worst case number of such hypotheses grows as a polynomial in the sequence length. We show that the number of hypotheses in strongly-connected trackable models is bounded by a constant and give an expression for this constant. We also consider the problem of reconstructing which branch was taken at a node with same-colored out-neighbors, and show that it is always eventually possible to identify which branch was taken if the model is strongly connected and trackable. We illustrate these properties by assigning transition probabilities and employing standard tools for analyzing Markov chains. In addition, we present new results for the entropy rates of weak models according to whether they are trackable or not. These theorems indicate that the combination of trackability and strong connectivity dramatically simplifies the task of reconstructing which nodes were visited. This work has implications for any problem which can be described in terms of an agent traversing a colored graph, such as the reconstruction of hidden states in a hidden Markov model (HMM).

Approximate linear programs (ALPs) are well-known models based on value function approximations (VFAs) to obtain heuristic policies and lower bounds on the optimal policy cost of Markov decision processes (MDPs). The ALP VFA is a linear combination of predefined basis functions that are chosen using domain knowledge and updated heuristically if the ALP optimality gap is large. We side-step the need for such basis function engineering in ALP -- an implementation bottleneck -- by proposing a sequence of ALPs that embed increasing numbers of random basis functions obtained via inexpensive sampling. We provide a sampling guarantee and show that the VFAs from this sequence of models converge to the exact value function. Nevertheless, the performance of the ALP policy can fluctuate significantly as more basis functions are sampled. To mitigate these fluctuations, we "self-guide" our convergent sequence of ALPs using past VFA information such that a worst-case measure of policy performance is improved. We perform numerical experiments on perishable inventory control and generalized joint replenishment applications, which, respectively, give rise to challenging discounted-cost MDPs and average-cost semi-MDPs. We find that self-guided ALPs (i) significantly reduce policy cost fluctuations and improve the optimality gaps from an ALP approach that employs basis functions tailored to the former application, and (ii) deliver optimality gaps that are comparable to a known adaptive basis function generation approach targeting the latter application. More broadly, our methodology provides application-agnostic policies and lower bounds to benchmark approaches that exploit application structure.