We present DEPS, an end-to-end algorithm for discovering parameterized skills from expert demonstrations. Our method learns parameterized skill policies jointly with a meta-policy that selects the appropriate discrete skill and continuous parameters at each timestep. Using a combination of temporal variational inference and information-theoretic regularization methods, we address the challenge of degeneracy common in latent variable models, ensuring that the learned skills are temporally extended, semantically meaningful, and adaptable. We empirically show that learning parameterized skills from multitask expert demonstrations significantly improves generalization to unseen tasks. Our method outperforms multitask as well as skill learning baselines on both LIBERO and MetaWorld benchmarks. We also demonstrate that DEPS discovers interpretable parameterized skills, such as an object grasping skill whose continuous arguments define the grasp location.

Asymptotically tight lower bounds are derived for the Input/Output (I/O) complexity of a class of dynamic programming algorithms, including matrix chain multiplication, optimal polygon triangulation, and the construction of optimal binary search trees. Assuming no recomputation of intermediate values, we establish an Ω(n³/(√M B)) I/O lower bound, where n denotes the size of the input and M denotes the size of the available fast memory (cache). When recomputation is allowed, we show that the same bound holds for M < cn, where c is a positive constant. In the case where M ≥ 2n, we show an Ω(n/B) I/O lower bound. We also discuss algorithms for which the number of executed I/O operations matches asymptotically each of the presented lower bounds, which are thus asymptotically tight. Additionally, we refine our general method to obtain a lower bound for the I/O complexity of the Cocke-Younger-Kasami algorithm, where the size of the grammar impacts the I/O complexity. An upper bound with asymptotically matching performance in many cases is also provided.

Real-world robot task planning is intractable in part due to partial observability. A common approach to reducing complexity is introducing additional structure into the decision process, such as mixed-observability, factored states, or temporally-extended actions. We propose the locally observable Markov decision process, a novel formulation that models task-level planning where uncertainty pertains to object-level attributes and where a robot has subroutines for seeking and accurately observing objects. This models sensors that are range-limited and line-of-sight—objects occluded or outside sensor range are unobserved, but the attributes of objects that fall within sensor view can be resolved via repeated observation. Our model results in a three-stage planning process: first, the robot plans using only observed objects; if that fails, it generates a target object that, if observed, could result in a feasible plan; finally, it attempts to locate and observe the target, replanning after each newly observed object. By combining LOMDPs with off-the-shelf Markov planners, we outperform state-of-the-art-solvers for both object-oriented POMDP and MDP analogues with the same task specification. We then apply the formulation to successfully solve a task on a mobile robot.