4,798 research outputs found
Probably Approximately Correct MDP Learning and Control With Temporal Logic Constraints
We consider synthesis of control policies that maximize the probability of
satisfying given temporal logic specifications in unknown, stochastic
environments. We model the interaction between the system and its environment
as a Markov decision process (MDP) with initially unknown transition
probabilities. The solution we develop builds on the so-called model-based
probably approximately correct Markov decision process (PAC-MDP) methodology.
The algorithm attains an -approximately optimal policy with
probability using samples (i.e. observations), time and space that
grow polynomially with the size of the MDP, the size of the automaton
expressing the temporal logic specification, ,
and a finite time horizon. In this approach, the system
maintains a model of the initially unknown MDP, and constructs a product MDP
based on its learned model and the specification automaton that expresses the
temporal logic constraints. During execution, the policy is iteratively updated
using observation of the transitions taken by the system. The iteration
terminates in finitely many steps. With high probability, the resulting policy
is such that, for any state, the difference between the probability of
satisfying the specification under this policy and the optimal one is within a
predefined bound.Comment: 9 pages, 5 figures, Accepted by 2014 Robotics: Science and Systems
(RSS
From the Quantum Approximate Optimization Algorithm to a Quantum Alternating Operator Ansatz
The next few years will be exciting as prototype universal quantum processors
emerge, enabling implementation of a wider variety of algorithms. Of particular
interest are quantum heuristics, which require experimentation on quantum
hardware for their evaluation, and which have the potential to significantly
expand the breadth of quantum computing applications. A leading candidate is
Farhi et al.'s Quantum Approximate Optimization Algorithm, which alternates
between applying a cost-function-based Hamiltonian and a mixing Hamiltonian.
Here, we extend this framework to allow alternation between more general
families of operators. The essence of this extension, the Quantum Alternating
Operator Ansatz, is the consideration of general parametrized families of
unitaries rather than only those corresponding to the time-evolution under a
fixed local Hamiltonian for a time specified by the parameter. This ansatz
supports the representation of a larger, and potentially more useful, set of
states than the original formulation, with potential long-term impact on a
broad array of application areas. For cases that call for mixing only within a
desired subspace, refocusing on unitaries rather than Hamiltonians enables more
efficiently implementable mixers than was possible in the original framework.
Such mixers are particularly useful for optimization problems with hard
constraints that must always be satisfied, defining a feasible subspace, and
soft constraints whose violation we wish to minimize. More efficient
implementation enables earlier experimental exploration of an alternating
operator approach to a wide variety of approximate optimization, exact
optimization, and sampling problems. Here, we introduce the Quantum Alternating
Operator Ansatz, lay out design criteria for mixing operators, detail mappings
for eight problems, and provide brief descriptions of mappings for diverse
problems.Comment: 51 pages, 2 figures. Revised to match journal pape
Grounding semantics in robots for Visual Question Answering
In this thesis I describe an operational implementation of an object detection and description system that incorporates in an end-to-end Visual Question Answering system and evaluated it on two visual question answering datasets for compositional language and elementary visual reasoning
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