On exploiting spectral properties for solving MDP with large state space

Liu, Li-Bin; Chattopadhyay, Arpan; Mitra, Urbashi

doi:10.1109/allerton.2017.8262875

Cited by 8 publications

(5 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Optimizing this function in the process of mapping an unknown environment, where the objective model and the time needed to build it are unknown, is still under research. Though the process of predicting the future impact of an action is computationally expensive, there are recent advancements by using spectral techniques [ 163 ] and deep learning [ 164 ].…”

Section: On Going Developmentsmentioning

confidence: 99%

Active Mapping and Robot Exploration: A Survey

Lluvia

Lazkano

Ansuategi

2021

Sensors

View full text Add to dashboard Cite

Simultaneous localization and mapping responds to the problem of building a map of the environment without any prior information and based on the data obtained from one or more sensors. In most situations, the robot is driven by a human operator, but some systems are capable of navigating autonomously while mapping, which is called native simultaneous localization and mapping. This strategy focuses on actively calculating the trajectories to explore the environment while building a map with a minimum error. In this paper, a comprehensive review of the research work developed in this field is provided, targeting the most relevant contributions in indoor mobile robotics.

show abstract

Section: On Going Developmentsmentioning

confidence: 99%

Active Mapping and Robot Exploration: A Survey

Lluvia

Lazkano

Ansuategi

2021

Sensors

View full text Add to dashboard Cite

show abstract

“…In the first category, the system itself is approximated by a low-complexity system (e.g., smaller dimension), whereas an approximately optimal solution can be obtained. Methods in this category include bisimulation [13], [6], PCA analysis [26], [20], and information-theoretic compression such as the information bottleneck method [1], [17]. In the second category, a low-complexity policy is instead obtained directly.…”

Section: B Contributionmentioning

confidence: 99%

Computing Complexity-aware Plans Using Kolmogorov Complexity

Stefansson¹,

Johansson²

2021

Preprint

View full text Add to dashboard Cite

In this paper, we introduce complexity-aware planning for finite-horizon deterministic finite automata with rewards as outputs, based on Kolmogorov complexity. Kolmogorov complexity is considered since it can detect computational regularities of deterministic optimal policies. We present a planning objective yielding an explicit trade-off between a policy's performance and complexity. It is proven that maximising this objective is non-trivial in the sense that dynamic programming is infeasible. We present two algorithms obtaining low-complexity policies, where the first algorithm obtains a lowcomplexity optimal policy, and the second algorithm finds a policy maximising performance while maintaining local (stagewise) complexity constraints. We evaluate the algorithms on a simple navigation task for a mobile robot, where our algorithms yield low-complexity policies that concur with intuition.

show abstract

“…3 Result on the spectral value iteration algorithm Using the notation of [1], we are calling • P µ is the state transition matrix under policy µ, such that P µ ∞ = 1.…”

Section: Spectral Radiusmentioning

confidence: 99%

“…The article [1] introduces a method to generalize the value iteration algorithm, which becomes computationally unfeasible for MDPs with large state-space. This algorithm requires run the value iteration algorithm on a subspace of the state space that is chosen according to the spectral properties of the probability transition matrix of the process.…”

Section: Introductionmentioning

confidence: 99%