@article{12511,
  abstract     = {We consider the problem of formally verifying almost-sure (a.s.) asymptotic stability in discrete-time nonlinear stochastic control systems. While verifying stability in deterministic control systems is extensively studied in the literature, verifying stability in stochastic control systems is an open problem. The few existing works on this topic either consider only specialized forms of stochasticity or make restrictive assumptions on the system, rendering them inapplicable to learning algorithms with neural network policies. 
 In this work, we present an approach for general nonlinear stochastic control problems with two novel aspects: (a) instead of classical stochastic extensions of Lyapunov functions, we use ranking supermartingales (RSMs) to certify a.s. asymptotic stability, and (b) we present a method for learning neural network RSMs. 
 We prove that our approach guarantees a.s. asymptotic stability of the system and
 provides the first method to obtain bounds on the stabilization time, which stochastic Lyapunov functions do not.
 Finally, we validate our approach experimentally on a set of nonlinear stochastic reinforcement learning environments with neural network policies.},
  author       = {Lechner, Mathias and Zikelic, Dorde and Chatterjee, Krishnendu and Henzinger, Thomas A},
  isbn         = {9781577358350},
  issn         = {2374-3468},
  journal      = {Proceedings of the AAAI Conference on Artificial Intelligence},
  keywords     = {General Medicine},
  number       = {7},
  pages        = {7326--7336},
  publisher    = {Association for the Advancement of Artificial Intelligence},
  title        = {{Stability verification in stochastic control systems via neural network supermartingales}},
  doi          = {10.1609/aaai.v36i7.20695},
  volume       = {36},
  year         = {2022},
}

@article{9197,
  abstract     = {In this paper we introduce and study all-pay bidding games, a class of two player, zero-sum games on graphs. The game proceeds as follows. We place a token on some vertex in the graph and assign budgets to the two players. Each turn, each player submits a sealed legal bid (non-negative and below their remaining budget), which is deducted from their budget and the highest bidder moves the token onto an adjacent vertex. The game ends once a sink is reached, and Player 1 pays Player 2 the outcome that is associated with the sink. The players attempt to maximize their expected outcome. Our games model settings where effort (of no inherent value) needs to be invested in an ongoing and stateful manner. On the negative side, we show that even in simple games on DAGs, optimal strategies may require a distribution over bids with infinite support. A central quantity in bidding games is the ratio of the players budgets. On the positive side, we show a simple FPTAS for DAGs, that, for each budget ratio, outputs an approximation for the optimal strategy for that ratio. We also implement it, show that it performs well, and suggests interesting properties of these games. Then, given an outcome c, we show an algorithm for finding the necessary and sufficient initial ratio for guaranteeing outcome c with probability 1 and a strategy ensuring such. Finally, while the general case has not previously been studied, solving the specific game in which Player 1 wins iff he wins the first two auctions, has been long stated as an open question, which we solve.},
  author       = {Avni, Guy and Ibsen-Jensen, Rasmus and Tkadlec, Josef},
  isbn         = {9781577358350},
  issn         = {2374-3468},
  journal      = {Proceedings of the AAAI Conference on Artificial Intelligence},
  location     = {New York, NY, United States},
  number       = {02},
  pages        = {1798--1805},
  publisher    = {Association for the Advancement of Artificial Intelligence},
  title        = {{All-pay bidding games on graphs}},
  doi          = {10.1609/aaai.v34i02.5546},
  volume       = {34},
  year         = {2020},
}

@inproceedings{14186,
  abstract     = {The goal of the unsupervised learning of disentangled representations is to
separate the independent explanatory factors of variation in the data without
access to supervision. In this paper, we summarize the results of Locatello et
al., 2019, and focus on their implications for practitioners. We discuss the
theoretical result showing that the unsupervised learning of disentangled
representations is fundamentally impossible without inductive biases and the
practical challenges it entails. Finally, we comment on our experimental
findings, highlighting the limitations of state-of-the-art approaches and
directions for future research.},
  author       = {Locatello, Francesco and Bauer, Stefan and Lucic, Mario and Rätsch, Gunnar and Gelly, Sylvain and Schölkopf, Bernhard and Bachem, Olivier},
  booktitle    = {The 34th AAAI Conference on Artificial Intelligence},
  isbn         = {9781577358350},
  issn         = {2374-3468},
  location     = {New York, NY, United States},
  number       = {9},
  pages        = {13681--13684},
  publisher    = {Association for the Advancement of Artificial Intelligence},
  title        = {{A commentary on the unsupervised learning of disentangled representations}},
  doi          = {10.1609/aaai.v34i09.7120},
  volume       = {34},
  year         = {2020},
}