Selected papers
 Toward negotiable reinforcement learning: shifting priorities in Pareto optimal sequential decisionmaking(2017, under review)
 Description
 BibTeX
 latest pdf
 arxiv
Exhibits a recursive formula for characterizing how a Paretooptimal policy, as judged by players with common knowledge of differing beliefs and values, must provably obey over time.  Logical Inductors(2016, under review)
 Description
 BibTeX
@misc{Gar16, author="Scott Garrabrant, Tsvi Benson Tilsen, Andrew Critch, Nate Soares, Jessica Taylor", title = "{Logical Induction}", year = {2016}, howpublished = "{arXiv:1609.03543}", }
 arXiv
 abridged pdf
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Presents an algorithm which assigns probabilities to mathematical statements using Brouwer’s fixed point theorem, in a wellcalibrated, selfconsistent manner, long before proofs verifying or refuting the statements can be found. The algorithm predicts the outputs of computations in a wellcalibrated way, including its own outputs. It is also has reasonable beliefs about itself (as a mathematical object), including accurate beliefs about its own approximate consistency, and beliefs that its future beliefs are more accurate than its current beliefs. All these properties follow from a single, elegant criterion, which makes them highly natural as criteria for “good reasoning” for a bounded reasoner thinking about mathematics, and in particular, computations.  Parametric Bounded Löb’s Theorem and Robust Cooperation of Bounded Agents(2016, under review)
 Description
 BibTeX
@misc{Cri16, author="Andrew J. Critch", title = "{Parametric Bounded Lob's Theorem and Robust Cooperation of Bounded Agents}", year = {2016}, howpublished = "{arXiv:1602.04184}", }
 arXiv
Establishes a bounded version of Löb’s theorem applicable to (computable) algorithms. The result is then used to demonstrate the existence of various algorithmic agents which robustly cooperate with one another on a singeinstance Prisoner’s Dilemma when they “know who heir opponent is”, with no incentive for either agent to defect. This result departs from the classical Nash equilibrium solution (D,D) for classically rational agents, illustrating that the framework of classical game theory is not adequate for agents that reason about one another’s source codes.  Algebraic Geometry of Matrix Product Stateswith Jason Morton (2012), in SIGMA 10 (2014), 095, 10 pages
 Description
We exhibit polynomial constraints on classes of representations of entangled qubits as matrix product states.
 BibTeX
@article{critch2014algebraic, title={Algebraic geometry of matrix product states}, author={Critch, Andrew and Morton, Jason}, journal={SIGMA}, volume={10}, number={095}, pages={095}, year={2014} }
 arXiv
 SIGMA
 Description
 Binary hidden Markov models and varieties(2012), in the Journal of Algebraic Statistics, Vol . 4, No. 1, 2013.
 A note on the proportionality between some consistency indices in the AHPwith Matteo Brunelli and Michele Fedrizzi (2010), in Applied Mathematics and Computation.
 Pushing the limit (generalized limits and limit extrema in topology)in the Atlantic Electronic Journal of Mathematics, vol. 1, iss. 1 (2006), pp. 4755.
 Resolving the BanachTarski paradox: inseparability of rigid bodies
@misc{BCF10,
author="Matteo Brunelli and Andrew J. Critch and Michele Fedrizzi",
title = "{A note on the proportionality between some consistency indices in the AHP}",
year = {2010},
howpublished = "{arXiv:1203.6431v1}",
}
@article{Cri06a,
author="{Andrew J. Critch}",
title="{Generalized limits and limit extrema}",
journal="Atlantic Electronic Journal of Mathematics",
year={2006},
volume={1},
number={1},
pages={47  55},
}
@misc{Cri06b,
author="{Andrew J. Critch}",
title = "{Resolving the BanachTarski paradox: inseparability of rigid bodies}",
year = {2006},
howpublished = "{B.Sc. Honors thesis, Memorial University of Newfoundland}",
}
Software
 Robust Rental Harmonywith Jacob Tsimerman and Chelsea Voss (2015) A novel algorithm and accompanying webapp interface for splitting rent in a robustly envyfree way between housemates.
 Tensors.m2with Claudiu Raicu (2012), began at the WFU2012 Macaulay2 developers workshop. A Macaulay2 package for studying varieties of tensors and tensor networks.
 Credence Calibration Gamewith Alexei Andreev and Zachary Alethia (2012). A game using informationtheoretic scoring to calibrate players’ subjective belief strengths to more accurately match their success rates.
Selected talks
 Logical inductors(September, 2016) at the MIRI graduate student seminar
 Superintelligence – technical (and nontechnical) problems in longterm AI Safety(November, 2015) in the Oxford Future of Humanity Institute’s Graduate Lecture Series
 Unexpected Expectations – probabilistic methods in combinatorics(June, 2015) with Evan Chen, for the Canadian IMO team Summer Camp
 Algebraic constraints on MPSentangled qubits(September, 2012) in the RTG workshop on Tensors and their Geometry in High Dimensions at UC Berkeley
 Causality and algebraic geometry(September, 2012) in the Queen’s Algebraic Geometry Seminar
 A new parametrization for binary hidden Markov models(June, 2012) at Algebraic Statistics in the Alleghenies, Pennsylvania State University
 Computing examples in algebraic geometry(January, 2012) in the Student Algebraic Geometry Seminar, UC Berkeley
 What causality is (stats for mathematicians)(August, 2011) in the Berkeley Algebraic Statistics Seminar
 Picard group of the moduli stack of elliptic curves
(an introduction to stacks by example)(March, 2011) in the Student Algebraic Geometry Seminar, UC Berkeley
Other research activities

(June, 2016) With Tom Dietterich, Percy Liang, Jacob Steinhardt, and Jessica Taylor.
 UC Berkeley Provability, DecisionTheory and Artificial Intelligence Seminar(Fall, 2015) Coorganized the seminar with Tsvi BensonTilsen.
 Berkeley Student Algebraic Geometry Seminar(Spring 2011 – Spring 2012) Coorganized the seminar, first with Charley Crissman, and later with Andrew Dudzik.
 COGS Causal Inference Symposium(February, 2012) Coorganized the symposium with Mike Pacer.
 Berkeley Algebraic Statistics Seminar(Fall 2011) Coorganized the seminar with Shaowei Lin.