(Near) Optimal Adaptivity Gaps for Stochastic Multi-Value Probing

Consider a kidney-exchange application where we want to find a max-matching in a random graph. To find whether an edge e exists, we need to perform an expensive test, in which case the edge e appears independently with a known probability p_e. Given a budget on the total cost of the tests, our goal is to find a testing strategy that maximizes the expected maximum matching size. The above application is an example of the stochastic probing problem. In general the optimal stochastic probing strategy is difficult to find because it is adaptive - decides on the next edge to probe based on the outcomes of the probed edges. An alternate approach is to show the adaptivity gap is small, i.e., the best non-adaptive strategy always has a value close to the best adaptive strategy. This allows us to focus on designing non-adaptive strategies that are much simpler. Previous works, however, have focused on Bernoulli random variables that can only capture whether an edge appears or not. In this work we introduce a multi-value stochastic probing problem, which can also model situations where the weight of an edge has a probability distribution over multiple values. Our main technical contribution is to obtain (near) optimal bounds for the (worst-case) adaptivity gaps for multi-value stochastic probing over prefix-closed constraints. For a monotone submodular function, we show the adaptivity gap is at most 2 and provide a matching lower bound. For a weighted rank function of a k-extendible system (a generalization of intersection of k matroids), we show the adaptivity gap is between O(k log k) and k. None of these results were known even in the Bernoulli case where both our upper and lower bounds also apply, thereby resolving an open question of Gupta et al. [Gupta et al., 2017]

Multistage Stochastic Portfolio Optimisation in Deregulated Electricity Markets Using Linear Decision Rules

The deregulation of electricity markets increases the financial risk faced by retailers who procure electric energy on the spot market to meet their customers’ electricity demand. To hedge against this exposure, retailers often hold a portfolio of electricity derivative contracts. In this paper, we propose a multistage stochastic mean-variance optimisation model for the management of such a portfolio. To reduce computational complexity, we perform two approximations: stage-aggregation and linear decision rules (LDR). The LDR approach consists of restricting the set of decision rules to those affine in the history of the random parameters. When applied to mean-variance optimisation models, it leads to convex quadratic programs. Since their size grows typically only polynomially with the number of periods, they can be efficiently solved. Our numerical experiments illustrate the value of adaptivity inherent in the LDR method and its potential for enabling scalability to problems with many periods.OR in energy, electricity portfolio management, stochastic programming, risk management, linear decision rules

A molecular approach to complex adaptive systems

Complex Adaptive Systems (CAS) are dynamical networks of interacting agents which as a whole determine the behavior, adaptivity and cognitive ability of the system. CAS are ubiquitous and occur in a variety of natural and artificial systems (e.g., cells, societies, stock markets). To study CAS, Holland proposed to employ an agent-based system in which Learning Classifier Systems (LCS) were used to determine the agents behavior and adaptivity. We argue that LCS are limited for the study of CAS: the rule-discovery mechanism is pre-specified and may limit the evolvability of CAS. Secondly, LCS distinguish a demarcation between messages and rules, however operations are reflexive in CAS, e.g., in a cell, an agent (a molecule) may both act as a message (substrate) and as a catalyst (rule). To address these issues, we proposed the Molecular Classifier Systems (MCS.b), a string-based Artificial Chemistry based on Holland’s broadcast language. In the MCS.b, no explicit fitness function or rule discovery mechanism is specified, moreover no distinction is made between messages and rules. In the context of the ESIGNET project, we employ the MCS.b to study a subclass of CAS: Cell Signaling Networks (CSNs) which are complex biochemical networks responsible for coordinating cellular activities. As CSNs occur in cells, these networks must replicate themselves prior to cell division. In this paper we present a series of experiments focusing on the self-replication ability of these CAS. Results indicate counter intuitive outcomes as opposed to those inferred from the literature. This work highlights the current deficit of a theoretical framework for the study of Artificial Chemistries

PHASE, a Monte Carlo event generator for six-fermion physics at the LHC

PHASE is a new event generator dedicated to the study of Standard Model processes with six fermions in the final state at the LHC. The code is intended for analyses of vector boson scattering, Higgs search, three gauge boson production, and top physics. This first version of the program describes final states characterized by the presence of one neutrino, $pp\to 4q +l\nu_l$, at O($\alpha^6$). PHASE is based on a new iterative-adaptive multichannel technique, and employs exact leading order matrix elements. The code can generate unweighted events for any subset of all available final states. The produced parton-level events carry full information on their colour and flavour structure, enabling the evolution of the partons into fully hadronised final states. An interface to hadronization packages is provided via the Les Houches Protocol.Comment: 27 pages, Latex, 6 figure