Barrier Certificates for Assured Machine Teaching

@article{Ahmadi2019BarrierCF,
  title={Barrier Certificates for Assured Machine Teaching},
  author={Mohamadreza Ahmadi and B. Wu and Yuxin Chen and Yisong Yue and Ufuk Topcu},
  journal={2019 American Control Conference (ACC)},
  year={2019},
  pages={3658-3663}
}
  • M. AhmadiB. Wu U. Topcu
  • Published 28 September 2018
  • Computer Science
  • 2019 American Control Conference (ACC)
Machine teaching can be viewed as optimal control for learning. Given a learner's model, machine teaching aims to determine the optimal training data to steer the learner towards a target hypothesis. In this paper, we are interested in providing assurances for machine teaching algorithms using control theory. In particular, we study a well-established learner's model in the machine teaching literature that is captured by the local preference over a version space. We interpret the problem of… 

Figures from this paper

Safe Policy Synthesis in Multi-Agent POMDPs via Discrete-Time Barrier Functions

This paper uses barrier functions to design policies for MPOMDPs that ensure safety and forms sufficient and necessary conditions for the safety of a given set based on discrete-time barrier functions (DTBFs) and demonstrates that the formulation also allows for Boolean compositions of DTBFs for representing more complicated safe sets.

Control Theory Meets POMDPs: A Hybrid Systems Approach

A barrier certificate theorem is formulated, wherein it is shown that if there exists a barrier certificate satisfying a set of inequalities along the solutions to the belief update equation of the POMDP, the safety and performance properties are guaranteed to hold.

Cost-Bounded Active Classification Using Partially Observable Markov Decision Processes

This work presents a decision-theoretic framework based on partially observable Markov decision processes (POMDPs) that relies on assigning a classification belief to each candidate MDP model, and designs POMDP strategies leading to classification decisions.

Locality Sensitive Teaching

A novel teaching framework, Locality Sensitive Teaching (LST), based on locality sensitive sampling, which has provable near-constant time complexity, which is exponentially better than the existing baseline and is readily applicable in real-world education scenarios.

References

SHOWING 1-10 OF 34 REFERENCES

An Optimal Control Approach to Sequential Machine Teaching

This work presents the first principled way to find the shortest training sequence to drive the learning algorithm to the target model, and studies the Pontryagin Maximum Principle, which yields a necessary condition for optimality of a training sequence.

Verification of Uncertain POMDPs Using Barrier Certificates

This work casts the POMDP problem into a switched system scenario, takes advantage of this switched system characterization and proposes a method based on barrier certificates for optimality and/or safety verification, and shows that the verification task can be carried out computationally by sum-of-squares programming.

Understanding the Role of Adaptivity in Machine Teaching: The Case of Version Space Learners

Inspired by human teaching, a new model where the learner picks hypotheses according to some local preference defined by the current hypothesis is proposed, and it is shown that the model exhibits several desirable properties, e.g., adaptivity plays a key role, and theLearner’s transitions over hypotheses are smooth/interpretable.

On the complexity of teaching

This paper studies the complexity of teaching by considering a variant of the on-line learning model in which a helpful teacher selects the instances, and measures the teaching dimension by a combinatorial measure.

Preference-based Teaching

We introduce a new model of teaching named "preference-based teaching" and a corresponding complexity parameter--the preference-based teaching dimension (PBTD)--representing the worstcase number of

LMI Techniques for Optimization Over Polynomials in Control: A Survey

  • G. Chesi
  • Computer Science, Mathematics
    IEEE Transactions on Automatic Control
  • 2010
This survey aims to provide the reader with a significant overview of the LMI techniques that are used in control systems for tackling optimization problems over polynomials, describing approaches such as decomposition in sum of squares, Positivstellensatz, theory of moments, Pólya's theorem, and matrix dilation.

Privacy Verification in POMDPs via Barrier Certificates

It is demonstrated that, for MDPs and for POMDPs, privacy verification can be computationally implemented by solving a set of semi-definite programs and sum-of-squares programs, respectively.

Controller Synthesis for Safety of Physically-Viable Data-Driven Models

This work synthesizes a controller such that the evolution of the states avoid some pre-specified unsafe set over a given finite horizon and proposes a safety analysis theorem based on barrier certificates that can design controllers ensuring safety of the solutions to the data-driven differential inclusion over a finite horizon.

The Optimal Control of Partially Observable Markov Processes over the Infinite Horizon: Discounted Costs

The paper develops easily implemented approximations to stationary policies based on finitely transient policies and shows that the concave hull of an approximation can be included in the well-known Howard policy improvement algorithm with subsequent convergence.

Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization

In the first part of this thesis, we introduce a specific class of Linear Matrix Inequalities (LMI) whose optimal solution can be characterized exactly. This family corresponds to the case where the