Optimal Portfolio Using a Genetic Algorithm

Distributing the amount of money to invest in each stock of a portfolio, while maximizing profit and minimizing risk is key. This project applied the method of a genetic algorithm in order to select an optimal portfolio. A genetic algorithm generates solutions to optimization problems using techniques inspired by natural evolution. A five stock, five years’ portfolio was utilized in order to demonstrate the efficiency of a genetic algorithm. The most important steps of this method were the fitness function and the crossover. The fitness function is a formula that determined the effectiveness of the portfolio distribution; it returned a value for each portfolio distribution and the higher the value the better the distribution. The fitness function allowed us to rank and sort the generated distributions. Then, the crossover was performed in order to see how the genetic algorithm converges towards the optimal solution. The best portfolio distributions, according to the fitness function, were used for the crossover in order to generate even better distributions. Crossover was executed a couple of times by generating new generations of distributions, until the best distribution was produced. The best distribution produced a twenty-five percent average return and its computing time was eleven minutes

Easily Solving Dynamic Programming Problems in Haskell by Memoization of Hylomorphisms

Dynamic Programming is a well known algorithmic technique that solves problems by a combination of dividing a problem into subproblems and using memoization to avoid an exponential growth of the costs. We show how to implement Dynamic Programming in Haskell using a variation of hylomorphisms that includes memoization. Our implementation uses polymorphism so the same function can return the best score or the solution to the problem based on the type of the returned value

Performance Bounds in LpL_p norm for Approximate Value Iteration

International audienceApproximate Value Iteration (AVI) is a method for solving large Markov Decision Problems by approximating the optimal value function with a sequence of value function representations $V_n$ processed according to the iterations $V{n+1} = \mathcal{ATV}_n$ where $\mathcal{T}$ is the so-called Bellman operator and $\mathcal{A}$ an approximation operator, which may be implemented by a Supervised Learning (SL) algorithm. Usual bounds on the asymptotic performance of AVI are established in terms of the $L\infty$-norm approximation errors induced by the SL algorithm. However, most widely used SL algorithms (such as least squares regression) return a function (the best fit) that minimizes an empirical approximation error in $L_p$-norm $(p\geq1)$. In this paper, we extend the performance bounds of AVI to weighted $L_p$-norms, which enables to directly relate the performance of AVI to the approximation power of the SL algorithm, hence assuring the tightness and pratical relevance of these bounds. The main result is a performance bound of the resulting policies expressed in terms of the $L_p$-norm errors introduced by the successive approximations. The new bound takes into account a concentration coefficient that estimates how much the discounted future-state distributions starting from a probability measure used to assess the performance of AVI can possibly differ from the distribution used in the regression operation. We illustrate the tightness of the bounds on an optimal replacement problem

Development of One Day Probable Maximum Precipitation (PMP) and Isohyetal Map for Tigray Region, Ethiopia

Water is a prime requirement for the existence of life; however uncontrollable amounts of water can adversely affects the survival of living beings. Due to wide range of precipitation variability, drought and extreme floods, the study of one day Probable Maximum Precipitation (PMP) for Tigray region is necessary. In an attempt to develop PMP and Isohyetal map for one day duration, using annual daily extreme rainfall series of 22 stations were subjected to statistical analysis using Hershfield formula adapted version of chow. Stations having inadequate daily records were identified and estimated using Normal Ratio Method, and Double mass curve was employed to check for the consistency of the data. An appropriate frequency factor (Km) was displayed as a function of the mean of the annual maxima for rainfall observations and the PMP for one day duration, and the highest value of Km was found to be 5.91. It was found that PMP vary from 70.06 to 144.51 mm, and the ratio of estimated one-day PMP and highest observed rainfall varied from 1.04 to 1.42. To predict extreme daily rainfall for each station normal, log normal, log Pearson type-III and Gumbel probability distribution functions were used, and values were subjected to goodness of fit tests of  chi-square, correlation coefficient and coefficient of determination tests to assess how best the fits had been. Results revealed that the log Pearson type-III distribution performed the best, with average return period 2.7*103 years. The ratio of one-day PMP to rainfall depth for frequencies return period of 5, 10, 50, 100, 1000 and 10000 year floods had been estimated and found to vary from 33.29 to 175.92 mm. The predicted PMP value to depths of various years return period ratios were computed and found to vary between 0.5132 and 2.712. Isohyetal map over Tigray region was generated by means of Arc Map10, IDW interpolation approach and the PMP Isohyetal lines were vary from 80 to 135mm. The high PMP Isohyetal values were observed in the Southern, Central and Eastern Zone and decreases in South-East Zone. For more reliable finding it is better to deal with uniformly distributed stations and larger update data as the climate pattern of the region is dynamic. Keywords: PMP[1], Probability Distribution Function, Goodness of Fit Test, Return Period, Isohyetal Map, Tigray Region [1]Probable Maximum Precipitation-PM

Fast Low-Cost Estimation of Network Properties Using Random Walks

Abstract. We study the use of random walks as an efficient estimator of global properties of large undirected graphs, for example the number of edges, vertices, triangles, and generally, the number of small fixed subgraphs. We consider two methods based on first returns of random walks: the cycle formula of regenerative processes and weighted random walks with edge weights defined by the property under investigation. We review the theoretical foundations for these methods, and indicate how they can be adapted for the general non-intrusive investigation of large online networks. The expected value and variance of first return time of a random walk decrease with increasing vertex weight, so for a given time budget, re-turns to high weight vertices should give the best property estimates. We present theoretical and experimental results on the rate of convergence of the estimates as a function of the number of returns of a random walk to a given start vertex. We made experiments to estimate the number of vertices, edges and triangles, for two test graphs.

Improving the Practicality of Model-Based Reinforcement Learning: An Investigation into Scaling up Model-Based Methods in Online Settings

This thesis is a response to the current scarcity of practical model-based control algorithms in the reinforcement learning (RL) framework. As of yet there is no consensus on how best to integrate imperfect transition models into RL whilst mitigating policy improvement instabilities in online settings. Current state-of-the-art policy learning algorithms that surpass human performance often rely on model-free approaches that enjoy unmitigated sampling of transition data. Model-based RL (MBRL) instead attempts to distil experience into transition models that allow agents to plan new policies without needing to return to the environment and sample more data. The initial focus of this investigation is on kernel conditional mean embeddings (CMEs) (Song et al., 2009) deployed in an approximate policy iteration (API) algorithm (Grünewälder et al., 2012a). This existing MBRL algorithm boasts theoretically stable policy updates in continuous state and discrete action spaces. The Bellman operator’s value function and (transition) conditional expectation are modelled and embedded respectively as functions in a reproducing kernel Hilbert space (RKHS). The resulting finite-induced approximate pseudo-MDP (Yao et al., 2014a) can be solved exactly in a dynamic programming algorithm with policy improvement suboptimality guarantees. However model construction and policy planning scale cubically and quadratically respectively with the training set size, rendering the CME impractical for sampleabundant tasks in online settings. Three variants of CME API are investigated to strike a balance between stable policy updates and reduced computational complexity. The first variant models the value function and state-action representation explicitly in a parametric CME (PCME) algorithm with favourable computational complexity. However a soft conservative policy update technique is developed to mitigate policy learning oscillations in the planning process. The second variant returns to the non-parametric embedding and contributes (along with external work) to the compressed CME (CCME); a sparse and computationally more favourable CME. The final variant is a fully end-to-end differentiable embedding trained with stochastic gradient updates. The value function remains modelled in an RKHS such that backprop is driven by a non-parametric RKHS loss function. Actively compressed CME (ACCME) satisfies the pseudo-MDP contraction constraint using a sparse softmax activation function. The size of the pseudo-MDP (i.e. the size of the embedding’s last layer) is controlled by sparsifying the last layer weight matrix by extending the truncated gradient method (Langford et al., 2009) with group lasso updates in a novel ‘use it or lose it’ neuron pruning mechanism. Surprisingly this technique does not require extensive fine-tuning between control tasks

The role of the arts in professional education; making the invisible, visible.

'The purpose of art is washing the dust of daily life off our souls' (Pablo Picasso). This paper will explore the value of using the arts in professional education. We use the term arts to include all the creative arts, such as poetry, drama, music, fiction, film, television and all the visual arts. The general argument in our paper could be applied to education for a wide range of professionals, although we draw on examples from health, teaching, business, and law. Professional education, and particularly professional education which confers a licence to practice, is often tightly regulated and controlled by professional bodies, and curricula are generally employer-led. Students invest heavily in their education in most countries in the world, with a few enlightened and beleaguered countries constituting exceptions. In England, fees in most universities have risen almost threefold for entry in 2012. Globally, students expect a financial return on their investment in the form of a graduate job. Policy spanning decades and cutting across political parties has emphasised the production of employable graduates as the primary role of higher education. Our contention is that this has led to a significant narrowing of the focus of professional education. There is a difference, however, between creating a 'job-ready' graduate, who is able to fulfil a narrow set of immediate vocational requirements, and developing a creative critical thinker, who is able not merely to implement current best practice, but to challenge it, develop it and even overturn it if necessary and who will be able to function at the highest level if circumstances change and new challenges present themselves. Sheridan-Rabideau (2010, p. 56) argues that “there is both room and need for preparing more creative individuals in every discipline”. The paper offers a rationale for widening the curriculum so that it includes opportunities for imaginative and open ended work, via engagement with the arts. It draws on research projects that each of us has conducted and some under development. We will also draw on both theoretical literature and on literature offering examples of good practice in this area. We aim to show how the arts enable people to expand their thinking and feeling so that they can get to those things that are often invisible because they are difficult to express in conventional academic language. We will explore, for example, how the arts may stimulate playful approaches that can bypass inhibition and produce surprising and exceptional ideas, how they encourage the envisioning of alternatives , helping us to overturn thinking trammelled by routine, how they may promote empathy and a deeper understanding of those whom professionals try to help and support and how they might help professionals develop a resistance to hegemonic perspectives. Our argument is that professionals have to be able to get 'beyond the dust of daily life', rise above routines and protocols and think imaginatively and creatively

The Cost-Effectiveness of Alternative Instruments for Environmental Protection in a Second-Best Setting

This paper employs analytical and numerical general equilibrium models to examine the costs of achieving pollution reductions under a range of environmental policy instruments in a second-best setting with pre-existing factor taxes. We compare the costs and overall efficiency impacts of emissions taxes, emissions quotas, fuels taxes, performance standards, and mandated technologies, and explore how costs change with the magnitude of pre-existing taxes and the extent of pollution abatement. We find that the presence of distortionary taxes raises the costs of pollution abatement under each instrument relative to its costs in a first-best world. This extra cost is an increasing function of the magnitude of pre-existing tax rates. For plausible values of pre-existing tax rates and other parameters, the cost increase for all policies is substantial (35 percent or more). The impact of pre-existing taxes is particularly large for non-auctioned emissions quotas: here the cost increase can be several hundred percent. Earlier work on instrument choice has emphasized the potential reduction in compliance cost achievable by converting fixed emissions quotas into tradable emissions permits. Our results indicate that the regulator's decision whether to auction or grandfather emissions rights can have equally important cost impacts. Similarly, the choice as to how to recycle revenues from environmentally motivated taxes (whether to return the revenues in lump-sum fashion or via cuts in marginal tax rates) can be as important to cost as the decision whether the tax takes the form of an emissions tax or fuel tax, particularly when modest emissions reductions are involved. In both first- and second-best settings, the cost differences across instruments depend importantly on the extent of pollution abatement under consideration. Total abatement costs differ markedly at low levels of abatement. Strikingly, for all instruments except the fuel tax these costs converge to the same value as abatement levels approach 100 percent.