Percolation on uniform infinite planar maps

We construct the uniform infinite planar map (UIPM), obtained as the n \to \infty local limit of planar maps with n edges, chosen uniformly at random. We then describe how the UIPM can be sampled using a "peeling" process, in a similar way as for uniform triangulations. This process allows us to prove that for bond and site percolation on the UIPM, the percolation thresholds are p_c^bond=1/2 and p_c^site=2/3 respectively. This method also works for other classes of random infinite planar maps, and we show in particular that for bond percolation on the uniform infinite planar quadrangulation, the percolation threshold is p_c^bond=1/3.Comment: 26 pages, 9 figure

Learning Generative Models with Goal-conditioned Reinforcement Learning

We present a novel, alternative framework for learning generative models with goal-conditioned reinforcement learning. We define two agents, a goal conditioned agent (GC-agent) and a supervised agent (S-agent). Given a user-input initial state, the GC-agent learns to reconstruct the training set. In this context, elements in the training set are the goals. During training, the S-agent learns to imitate the GC-agent while remaining agnostic of the goals. At inference we generate new samples with the S-agent. Following a similar route as in variational auto-encoders, we derive an upper bound on the negative log-likelihood that consists of a reconstruction term and a divergence between the GC-agent policy and the (goal-agnostic) S-agent policy. We empirically demonstrate that our method is able to generate diverse and high quality samples in the task of image synthesis

Forced-exploration free Strategies for Unimodal Bandits

We consider a multi-armed bandit problem specified by a set of Gaussian or Bernoulli distributions endowed with a unimodal structure. Although this problem has been addressed in the literature (Combes and Proutiere, 2014), the state-of-the-art algorithms for such structure make appear a forced-exploration mechanism. We introduce IMED-UB, the first forced-exploration free strategy that exploits the unimodal-structure, by adapting to this setting the Indexed Minimum Empirical Divergence (IMED) strategy introduced by Honda and Takemura (2015). This strategy is proven optimal. We then derive KLUCB-UB, a KLUCB version of IMED-UB, which is also proven optimal. Owing to our proof technique, we are further able to provide a concise finite-time analysis of both strategies in an unified way. Numerical experiments show that both IMED-UB and KLUCB-UB perform similarly in practice and outperform the state-of-the-art algorithms

Finite element study of hyperstructure systems with modular light‐frame construction in high‐rise buildings

To answer both the growth of the world's urban population and the climate changes, new structural systems with high prefabrication levels and renewable materials need to be developed. A novel structural system that could enable the use of modular light‐frame construction in high‐rise buildings was modeled and analyzed. This system was achieved by having a hyperstructure carrying the loads of four‐story light‐frame superposed substructures. Two 20‐story hyperstructures, one using glulam and another one using reinforced concrete, were designed according to the 2015 National Building Code of Canada and compared. A simplified model for the light‐frame modules according to the CSA O86‐19 was proposed. The interaction between both systems and the impact on the substructures were analyzed. The results of the response spectrum analysis and dynamic wind analysis show that, with a glulam hyperstructure, modules could be connected to the columns and the floors or only to the floors. With a concrete hyperstructure, the modules must be connected to the columns and the cores. For both systems, the design of shearwalls on the short side of the modules is governed by the lateral deformation imposed by seismic forces, while the design of shearwalls on the long side of the modules is governed by the vertical deformation of the primary beams under gravity loads. Standard shearwall assemblies are sufficient to resist the shear induced by gravitational, wind and seismic loads. The analysis indicates that the system could be viable, but more research should be especially performed on the connections between the substructures and the hyperstructure

Gamification of Pure Exploration for Linear Bandits

We investigate an active pure-exploration setting, that includes best-arm identification, in the context of linear stochastic bandits. While asymptotically optimal algorithms exist for standard multi-arm bandits, the existence of such algorithms for the best-arm identification in linear bandits has been elusive despite several attempts to address it. First, we provide a thorough comparison and new insight over different notions of optimality in the linear case, including G-optimality, transductive optimality from optimal experimental design and asymptotic optimality. Second, we design the first asymptotically optimal algorithm for fixed-confidence pure exploration in linear bandits. As a consequence, our algorithm naturally bypasses the pitfall caused by a simple but difficult instance, that most prior algorithms had to be engineered to deal with explicitly. Finally, we avoid the need to fully solve an optimal design problem by providing an approach that entails an efficient implementation.Comment: 11+25 pages. To be published in the proceedings of ICML 202

Le remplacement des années vécues : une alternative à l'immigration et à la fécondité pour le remplacement des populations

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal