1,361 research outputs found
Solving Factored MDPs with Hybrid State and Action Variables
Efficient representations and solutions for large decision problems with
continuous and discrete variables are among the most important challenges faced
by the designers of automated decision support systems. In this paper, we
describe a novel hybrid factored Markov decision process (MDP) model that
allows for a compact representation of these problems, and a new hybrid
approximate linear programming (HALP) framework that permits their efficient
solutions. The central idea of HALP is to approximate the optimal value
function by a linear combination of basis functions and optimize its weights by
linear programming. We analyze both theoretical and computational aspects of
this approach, and demonstrate its scale-up potential on several hybrid
optimization problems
Efficient Constraint Generation for Stochastic Shortest Path Problems
Current methods for solving Stochastic Shortest Path Problems (SSPs) find
states' costs-to-go by applying Bellman backups, where state-of-the-art methods
employ heuristics to select states to back up and prune. A fundamental
limitation of these algorithms is their need to compute the cost-to-go for
every applicable action during each state backup, leading to unnecessary
computation for actions identified as sub-optimal. We present new connections
between planning and operations research and, using this framework, we address
this issue of unnecessary computation by introducing an efficient version of
constraint generation for SSPs. This technique allows algorithms to ignore
sub-optimal actions and avoid computing their costs-to-go. We also apply our
novel technique to iLAO* resulting in a new algorithm, CG-iLAO*. Our
experiments show that CG-iLAO* ignores up to 57% of iLAO*'s actions and it
solves problems up to 8x and 3x faster than LRTDP and iLAO*.Comment: Extended version of AAAI 2024 pape
Planning in Hybrid Structured Stochastic Domains
Efficient representations and solutions for large structured decision problems with continuous and discrete variables are among the important challenges faced by the designers of automated decision support systems. In this work, we describe a novel hybrid factored Markov decision process (MDP) model that allows for a compact representation of these problems, and a hybrid approximate linear programming (HALP) framework that permits their efficient solutions. The central idea of HALP is to approximate the optimal value function of an MDP by a linear combination of basis functions and optimize its weights by linear programming. We study both theoretical and practical aspects of this approach, and demonstrate its scale-up potential on several hybrid optimization problems
Numerical Integration and Dynamic Discretization in Heuristic Search Planning over Hybrid Domains
In this paper we look into the problem of planning over hybrid domains, where
change can be both discrete and instantaneous, or continuous over time. In
addition, it is required that each state on the trajectory induced by the
execution of plans complies with a given set of global constraints. We approach
the computation of plans for such domains as the problem of searching over a
deterministic state model. In this model, some of the successor states are
obtained by solving numerically the so-called initial value problem over a set
of ordinary differential equations (ODE) given by the current plan prefix.
These equations hold over time intervals whose duration is determined
dynamically, according to whether zero crossing events take place for a set of
invariant conditions. The resulting planner, FS+, incorporates these features
together with effective heuristic guidance. FS+ does not impose any of the
syntactic restrictions on process effects often found on the existing
literature on Hybrid Planning. A key concept of our approach is that a clear
separation is struck between planning and simulation time steps. The former is
the time allowed to observe the evolution of a given dynamical system before
committing to a future course of action, whilst the later is part of the model
of the environment. FS+ is shown to be a robust planner over a diverse set of
hybrid domains, taken from the existing literature on hybrid planning and
systems.Comment: 17 page
Extending classical planning with state constraints: Heuristics and search for optimal planning
We present a principled way of extending a classical AI planning formalism with systems of state constraints, which relate - sometimes determine - the values of variables in each state traversed by the plan. This extension occupies an attractive middle ground between expressivity and complexity. It enables modelling a new range of problems, as well as formulating more efficient models of classical planning problems. An example of the former is planning-based control of networked physical systems - power networks, for example - in which a local, discrete control action can have global effects on continuous quantities, such as altering flows across the entire network. At the same time, our extension remains decidable as long as the satisfiability of sets of state constraints is decidable, including in the presence of numeric state variables, and we demonstrate that effective techniques for cost-optimal planning known in the classical setting - in particular, relaxation-based admissible heuristics - can be adapted to the extended formalism. In this paper, we apply our approach to constraints in the form of linear or non-linear equations over numeric state variables, but the approach is independent of the type of state constraints, as long as there exists a procedure that decides their consistency. The planner and the constraint solver interact through a well-defined, narrow interface, in which the solver requires no specialisation to the planning contextThis work was supported by ARC project DP140104219, “Robust AI Planning for Hybrid Systems”, and in part by ARO grant W911NF1210471 and ONR grant N000141210430
Taming Numbers and Durations in the Model Checking Integrated Planning System
The Model Checking Integrated Planning System (MIPS) is a temporal least
commitment heuristic search planner based on a flexible object-oriented
workbench architecture. Its design clearly separates explicit and symbolic
directed exploration algorithms from the set of on-line and off-line computed
estimates and associated data structures. MIPS has shown distinguished
performance in the last two international planning competitions. In the last
event the description language was extended from pure propositional planning to
include numerical state variables, action durations, and plan quality objective
functions. Plans were no longer sequences of actions but time-stamped
schedules. As a participant of the fully automated track of the competition,
MIPS has proven to be a general system; in each track and every benchmark
domain it efficiently computed plans of remarkable quality. This article
introduces and analyzes the most important algorithmic novelties that were
necessary to tackle the new layers of expressiveness in the benchmark problems
and to achieve a high level of performance. The extensions include critical
path analysis of sequentially generated plans to generate corresponding optimal
parallel plans. The linear time algorithm to compute the parallel plan bypasses
known NP hardness results for partial ordering by scheduling plans with respect
to the set of actions and the imposed precedence relations. The efficiency of
this algorithm also allows us to improve the exploration guidance: for each
encountered planning state the corresponding approximate sequential plan is
scheduled. One major strength of MIPS is its static analysis phase that grounds
and simplifies parameterized predicates, functions and operators, that infers
knowledge to minimize the state description length, and that detects domain
object symmetries. The latter aspect is analyzed in detail. MIPS has been
developed to serve as a complete and optimal state space planner, with
admissible estimates, exploration engines and branching cuts. In the
competition version, however, certain performance compromises had to be made,
including floating point arithmetic, weighted heuristic search exploration
according to an inadmissible estimate and parameterized optimization
Belief-space Planning for Active Visual SLAM in Underwater Environments.
Autonomous mobile robots operating in a priori unknown environments must be able to integrate path planning with simultaneous localization and mapping (SLAM) in order to perform tasks like exploration, search and rescue, inspection, reconnaissance, target-tracking, and others. This level of autonomy is especially difficult in underwater environments, where GPS is unavailable, communication is limited, and environment features may be sparsely- distributed. In these situations, the path taken by the robot can drastically affect the performance of SLAM, so the robot must plan and act intelligently and efficiently to ensure successful task completion.
This document proposes novel research in belief-space planning for active visual SLAM in underwater environments. Our motivating application is ship hull inspection with an autonomous underwater robot. We design a Gaussian belief-space planning formulation that accounts for the randomness of the loop-closure measurements in visual SLAM and serves as the mathematical foundation for the research in this thesis. Combining this planning formulation with sampling-based techniques, we efficiently search for loop-closure actions throughout the environment and present a two-step approach for selecting revisit actions that results in an opportunistic active SLAM framework. The proposed active SLAM method is tested in hybrid simulations and real-world field trials of an underwater robot performing inspections of a physical modeling basin and a U.S. Coast Guard cutter.
To reduce computational load, we present research into efficient planning by compressing the representation and examining the structure of the underlying SLAM system. We propose the use of graph sparsification methods online to reduce complexity by planning with an approximate distribution that represents the original, full pose graph. We also propose the use of the Bayes tree data structure—first introduced for fast inference in SLAM—to perform efficient incremental updates when evaluating candidate plans that are similar. As a final contribution, we design risk-averse objective functions that account for the randomness within our planning formulation. We show that this aversion to uncertainty in the posterior belief leads to desirable and intuitive behavior within active SLAM.PhDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/133303/1/schaves_1.pd
Recommended from our members
A Framework for Globally Optimizing Mixed-Integer Signomial Programs
Mixed-integer signomial optimization problems have broad applicability in engineering. Extending the Global Mixed-Integer Quadratic Optimizer, GloMIQO (Misener, Floudas in J. Glob. Optim., 2012. doi:10.1007/s10898-012-9874-7), this manuscript documents a computational framework for deterministically addressing mixed-integer signomial optimization problems to ε-global optimality. This framework generalizes the GloMIQO strategies of (1) reformulating user input, (2) detecting special mathematical structure, and (3) globally optimizing the mixed-integer nonconvex program. Novel contributions of this paper include: flattening an expression tree towards term-based data structures; introducing additional nonconvex terms to interlink expressions; integrating a dynamic implementation of the reformulation-linearization technique into the branch-and-cut tree; designing term-based underestimators that specialize relaxation strategies according to variable bounds in the current tree node. Computational results are presented along with comparison of the computational framework to several state-of-the-art solvers. © 2013 Springer Science+Business Media New York
- …