In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.

[EX Q]: This paper presents the input convex neural network architecture. These are scalar-valued (potentially deep) neural networks with constraints on the network parameters such that the output of the network is a convex function of (some of) the inputs. The networks allow for efficient inference via optimization over some inputs to the network given others, and can be applied to settings including structured prediction, data imputation, reinforcement learning, and others. In this paper we lay the basic groundwork for these models, proposing methods for inference, optimization and learning, and analyze their representational power. We show that many existing neural network architectures can be made input-convex with only minor modification, and develop specialized optimization algorithms tailored to this setting. Finally, we highlight the performance of the methods on multi-label prediction, image completion, and reinforcement learning problems, where we show improvement over the existing state of the art in many cases.
[EX A]: Input Convex Neural Networks

[EX Q]: Reinforcement learning systems are often concerned with balancing exploration of untested actions against exploitation of actions that are known to be good. The benefit of exploration can be estimated using the classi­ cal notion of Value of Informationthe expected im­ provement in future decision quality arising from the tnformation acquired by exploration. Estimating this quantity requires an assessment of the agent's uncer­ tainty about its current value estimates for states. In this paper we investigate ways to represent and rea­ son about this uncertainty in algorithms where the sys­ tem attempts to learn a model of its environment. We explicitly represent uncertainty about the parameters of the model and build probability distributions over Q­ values based on these. These distributions are used to compute a myopic approximation to the value of infor­ mation for each action and hence to select the action that best balances exploration and exploitation.
[EX A]: Model based Bayesian Exploration

[EX Q]: In this paper we propose a structural parameter of CNF formulas and use it to identify instances of weighted MaxSAT and #SAT that can be solved in polynomial time. Given a CNF formula we say that a set of clauses is precisely satisfiable if there is some complete assignment satisfying these clauses only. Let the ps-value of the formula be the number of precisely satisfiable sets of clauses. Applying the notion of branch decompositions to CNF formulas and using ps-value as cut function, we define the ps-width of a formula. For a formula given with a decomposition of polynomial ps-width we show dynamic programming algorithms solving weighted MaxSAT and #SAT in polynomial time. Combining with results of ’Belmonte and Vatshelle, Graph classes with structured neighborhoods and algorithmic applications, Theor. Comput. Sci. 511: 54-65 (2013)’ we get polynomial-time algorithms solving weighted MaxSAT and #SAT for some classes of structured CNF formulas. For example, we get O(m(m + n)s) algorithms for formulas F of m clauses and n variables and size s, if F has a linear ordering of the variables and clauses such that for any variable x occurring in clause C, if x appears before C then any variable between them also occurs in C, and if C appears before x then x occurs also in any clause between them. Note that the class of incidence graphs of such formulas do not have bounded clique-width.
[EX A]:
Solving MaxSAT and #SAT on structured CNF formulas