We introduce a novel approach to hierarchical reinforcement learning for Linearly-solvable Markov Decision Processes (LMDPs) in the infinite-horizon average-reward setting. Unlike previous work, our approach allows learning low-level and high-level tasks simultaneously, without imposing limiting restrictions on the low-level tasks. Our method relies on partitions of the state space that create smaller subtasks that are easier to solve, and the equivalence between such partitions to learn more efficiently. We then exploit the compositionality of low-level tasks to exactly represent the value function of the high-level task. Experiments show that our approach can outperform flat average-reward reinforcement learning by one or several orders of magnitude.

Autonomous agents that interact with an environment usually To alleviate this issue, one can consider methods that condition face tasks that comprise complex, entangled behaviors over the policy or the value function on the specification of long horizons. Conventional reinforcement learning (RL) the whole task (Schaul et al. 2015) and such approaches were methods have successfully addressed this. However, in cases recently also proposed for tasks with non-Markovian reward when the agent is meant to perform several tasks across similar functions (Vaezipoor et al. 2021). However, the methods that environments, training a policy for every task separately specify the whole task usually rely on a blackbox neural network can be time-consuming and requires a lot of data. In such for planning when determining which sub-goal to reach cases, the agent can utilize a method that has built-in generalization next. This makes it hard to interpret the plan to solve the task capabilities. One such method relies on the assumption and although they show promising results in practice, it is that reward functions of these tasks can be decomposed unclear whether and when these approaches will generalize into a linear combination of successor features (Barreto et al. to a new task.

The challenge in combined task and motion planning (TAMP) is the effective integration of a search over a combinatorial space, usually carried out by a task planner, and a search over a continuous configuration space, carried out by a motion planner. Using motion planners for testing the feasibility of task plans and filling out the details is not effective because it makes the geometrical constraints play a passive role. This work introduces a new interleaved approach for integrating the two dimensions of TAMP that makes use of sketches, a recent simple but powerful language for expressing the decomposition of problems into subproblems. A sketch has width 1 if it decomposes the problem into subproblems that can be solved greedily in linear time. In the paper, a general sketch is introduced for several classes of TAMP problems which has width 1 under suitable assumptions. While sketch decompositions have been developed for classical planning, they offer two important benefits in the context of TAMP. First, when a task plan is found to be unfeasible due to the geometric constraints, the combinatorial search resumes in a specific sub-problem. Second, the sampling of object configurations is not done once, globally, at the start of the search, but locally, at the start of each subproblem. Optimizations of this basic setting are also considered and experimental results over existing and new pick-and-place benchmarks are reported.

We present a novel edge-level ego-network encoding for learning on graphs that can boost Message Passing Graph Neural Networks (MP-GNNs) by providing additional node and edge features or extending message-passing formats. The proposed encoding is sufficient to distinguish Strongly Regular Graphs, a family of challenging 3-WL equivalent graphs. We show theoretically that such encoding is more expressive than node-based sub-graph MP-GNNs. In an empirical evaluation on four benchmarks with 10 graph datasets, our results match or improve previous baselines on expressivity, graph classification, graph regression, and proximity tasks -- while reducing memory usage by 18.1x in certain real-world settings.

Identifying similar network structures is key to capture graph isomorphisms and learn representations that exploit structural information encoded in graph data. This work shows that ego-networks can produce a structural encoding scheme for arbitrary graphs with greater expressivity than the Weisfeiler-Lehman (1-WL) test. We introduce IGEL, a preprocessing step to produce features that augment node representations by encoding ego-networks into sparse vectors that enrich Message Passing (MP) Graph Neural Networks (GNNs) beyond 1-WL expressivity. We describe formally the relation between IGEL and 1-WL, and characterize its expressive power and limitations. Experiments show that IGEL matches the empirical expressivity of state-of-the-art methods on isomorphism detection while improving performance on seven GNN architectures.

In this work we present a novel approach to hierarchical reinforcement learning for linearly-solvable Markov decision processes. Our approach assumes that the state space is partitioned, and the subtasks consist in moving between the partitions. We represent value functions on several levels of abstraction, and use the compositionality of subtasks to estimate the optimal values of the states in each partition. The policy is implicitly defined on these optimal value estimates, rather than being decomposed among the subtasks. As a consequence, our approach can learn the globally optimal policy, and does not suffer from the non-stationarity of high-level decisions. If several partitions have equivalent dynamics, the subtasks of those partitions can be shared. If the set of boundary states is smaller than the entire state space, our approach can have significantly smaller sample complexity than that of a flat learner, and we validate this empirically in several experiments.

Width-based search methods have demonstrated state-of-the-art performance in a wide range of testbeds, from classical planning problems to image-based simulators such as Atari games. These methods scale independently of the size of the state-space, but exponentially in the problem width. In practice, running the algorithm with a width larger than 1 is computationally intractable, prohibiting IW from solving higher width problems. In this paper, we present a hierarchical algorithm that plans at two levels of abstraction. A high-level planner uses abstract features that are incrementally discovered from low-level pruning decisions. We illustrate this algorithm in classical planning PDDL domains as well as in pixel-based simulator domains. In classical planning, we show how IW(1) at two levels of abstraction can solve problems of width 2. For pixel-based domains, we show how in combination with a learned policy and a learned value function, the proposed hierarchical IW can outperform current flat IW-based planners in Atari games with sparse rewards.

Learning embeddings from large-scale networks is an open challenge. Despite the overwhelming number of existing methods, is is unclear how to exploit network structure in a way that generalizes easily to unseen nodes, edges or graphs. In this work, we look at the problem of finding inductive network embeddings in large networks without domain-dependent node/edge attributes. We propose to use a set of basic predefined local encodings as the basis of a learning algorithm. In particular, we consider the degree frequencies at different distances from a node, which can be computed efficiently for relatively short distances and a large number of nodes. Interestingly, the resulting embeddings generalize well across unseen or distant regions in the network, both in unsupervised settings, when combined with language model learning, as well as in supervised tasks, when used as additional features in a neural network. Despite its simplicity, this method achieves state-of-the-art performance in tasks such as role detection, link prediction and node classification, and represents an inductive network embedding method directly applicable to large unattributed networks.

On the other side of the spectrum, we observe that the data set with a lower log-likelihood is Noise, a data set of uniform random images, followed by TrafficSign and TinyImageNet; both featuring colorful images with nontrivial background. Such ordering is perhaps more clear by looking at the average log-likelihood of each data set (Appendix D). If we think about the visual complexity of the images in those data sets, it would seem that log-likelihoods tend to grow when images become simpler and with less information or content. To further confirm the previous observation, we design a controlled experiment where we can set different decreasing levels of image complexity. We train a generative model with some data set, as before, but now compute likelihoods of progressively simpler inputs. Such inputs are obtained by average-pooling the uniform random Noise images by factors of 1, 2, 4, 8, 16, and 32, and re-scaling back the images to the original size by nearest-neighbor up-sampling. Intuitively, a noise image with a pooling size of 1 (no pooling) has the highest complexity, while a noise image with a pooling of 32 (constant-color image) has the lowest complexity.

Ranking models are typically designed to provide rankings that optimize some measure of immediate utility to the users. As a result, they have been unable to anticipate an increasing number of undesirable long-term consequences of their proposed rankings, from fueling the spread of misinformation and increasing polarization to degrading social discourse. Can we design ranking models that understand the consequences of their proposed rankings and, more importantly, are able to avoid the undesirable ones? In this paper, we first introduce a joint representation of rankings and user dynamics using Markov decision processes. Then, we show that this representation greatly simplifies the construction of consequential ranking models that trade off the immediate utility and the long-term welfare. In particular, we can obtain optimal consequential rankings just by applying weighted sampling on the rankings provided by models that maximize measures of immediate utility. However, in practice, such a strategy may be inefficient and impractical, specially in high dimensional scenarios. To overcome this, we introduce an efficient gradient-based algorithm to learn parameterized consequential ranking models that effectively approximate optimal ones. We showcase our methodology using synthetic and real data gathered from Reddit and show that ranking models derived using our methodology provide ranks that may mitigate the spread of misinformation and improve the civility of online discussions.