Emulating Human Play in a Leading Mobile Card Game

Monte Carlo Tree Search (MCTS) has become a popular solution for game AI, capable of creating strong game playing opponents. However, the emergent playstyle of agents using MCTS is not neces- sarily human-like, believable or enjoyable. AI Factory Spades, currently the top rated Spades game in the Google Play store, uses a variant of MCTS to control AI allies and opponents. In collaboration with the developers, we showed in a previous study that the playstyle of human players significantly differed from that of the AI players [1]. This article presents a method for player modelling using gameplay data and neural networks that does not require domain knowledge, and a method of biasing MCTS with such a player model to create Spades playing agents that emulate human play whilst maintaining strong, competitive performance. The methods of player modelling and biasing MCTS presented in this study are applied to the commercial codebase of AI Factory Spades, and are transferable to MCTS implementations for discrete-action games where relevant gameplay data is available

Ullemar's formula for the Jacobian of the complex moment mapping

The complex moment sequence m(P) is assigned to a univalent polynomial P by the Cauchy transform of the P(D), where D is the unit disk. We establish the representation of the Jacobian det dm(P) in terms of roots of the derivative P'. Combining this result with the special decomposition for the Hurwitz determinants, we prove a formula for the Jacobian which was previously conjectured by C. Ullemar. As a consequence, we show that the boundary of the class of all locally univalent polynomials in $U$ is contained in the union of three irreducible algebraic surfaces.Comment: 14 pages, submitted for "Complex Variables. Theory and Application

An analysis of the Taguchi method for tuning a memetic algorithm with reduced computational time budget

Determining the best initial parameter values for an algorithm, called parameter tuning, is crucial to obtaining better algorithm performance; however, it is often a time-consuming task and needs to be performed under a restricted computational budget. In this study, the results from our previous work on using the Taguchi method to tune the parameters of a memetic algorithm for cross-domain search are further analysed and extended. Although the Taguchi method reduces the time spent finding a good parameter value combination by running a smaller size of experiments on the training instances from different domains as opposed to evaluating all combinations, the time budget is still larger than desired. This work investigates the degree to which it is possible to predict the same good parameter setting faster by using a reduced time budget. The results in this paper show that it was possible to predict good combinations of parameter settings with a much reduced time budget. The good final parameter values are predicted for three of the parameters, while for the fourth parameter there is no clear best value, so one of three similarly performing values is identified at each time instant

Performance of selection hyper-heuristics on the extended HyFlex domains

Selection hyper-heuristics perform search over the space of heuristics by mixing and controlling a predefined set of low level heuristics for solving computationally hard combinatorial optimisation problems. Being reusable methods, they are expected to be applicable to multiple problem domains, hence performing well in cross-domain search. HyFlex is a general purpose heuristic search API which separates the high level search control from the domain details enabling rapid development and performance comparison of heuristic search methods, particularly hyper-heuristics. In this study, the performance of six previously proposed selection hyper-heuristics are evaluated on three recently introduced extended HyFlex problem domains, namely 0–1 Knapsack, Quadratic Assignment and Max-Cut. The empirical results indicate the strong generalising capability of two adaptive selection hyper-heuristics which perform well across the ‘unseen’ problems in addition to the six standard HyFlex problem domains

Past, present, and future of global health financing: a review of development assistance, government, out-of-pocket, and other private spending on health for 195 countries, 1995–2050

© 2019 The Author(s). Published by Elsevier Ltd. This is an Open Access article under the CC BY 4.0 license Background: Comprehensive and comparable estimates of health spending in each country are a key input for health policy and planning, and are necessary to support the achievement of national and international health goals. Previous studies have tracked past and projected future health spending until 2040 and shown that, with economic development, countries tend to spend more on health per capita, with a decreasing share of spending from development assistance and out-of-pocket sources. We aimed to characterise the past, present, and predicted future of global health spending, with an emphasis on equity in spending across countries. Methods: We estimated domestic health spending for 195 countries and territories from 1995 to 2016, split into three categories—government, out-of-pocket, and prepaid private health spending—and estimated development assistance for health (DAH) from 1990 to 2018. We estimated future scenarios of health spending using an ensemble of linear mixed-effects models with time series specifications to project domestic health spending from 2017 through 2050 and DAH from 2019 through 2050. Data were extracted from a broad set of sources tracking health spending and revenue, and were standardised and converted to inflation-adjusted 2018 US dollars. Incomplete or low-quality data were modelled and uncertainty was estimated, leading to a complete data series of total, government, prepaid private, and out-of-pocket health spending, and DAH. Estimates are reported in 2018 US dollars, 2018 purchasing-power parity-adjusted dollars, and as a percentage of gross domestic product. We used demographic decomposition methods to assess a set of factors associated with changes in government health spending between 1995 and 2016 and to examine evidence to support the theory of the health financing transition. We projected two alternative future scenarios based on higher government health spending to assess the potential ability of governments to generate more resources for health. Findings: Between 1995 and 2016, health spending grew at a rate of 4·00% (95% uncertainty interval 3·89–4·12) annually, although it grew slower in per capita terms (2·72% [2·61–2·84]) and increased by less than $1 per capita over this period in 22 of 195 countries. The highest annual growth rates in per capita health spending were observed in upper-middle-income countries (5·55$8·0 trillion (7·8–8·1) in 2016 (comprising 8·6% [8·4–8·7] of the global economy and $10·3 trillion [10·1–10·6] in purchasing-power parity-adjusted dollars), with a per capita spending of US$5252 (5184–5319) in high-income countries, $491 (461–524) in upper-middle-income countries,$81 (74–89) in lower-middle-income countries, and $40 (38–43) in low-income countries. In 2016, 0·4$9·5 billion, 24·3% of total DAH), although spending on other infectious diseases (excluding tuberculosis and malaria) grew fastest from 2010 to 2018 (6·27% per year). The leading sources of DAH were the USA and private philanthropy (excluding corporate donations and the Bill & Melinda Gates Foundation). For the first time, we included estimates of China's contribution to DAH ($644·7 million in 2018). Globally, health spending is projected to increase to$15·0 trillion (14·0–16·0) by 2050 (reaching 9·4% [7·6–11·3] of the global economy and $21·3 trillion [19·8–23·1] in purchasing-power parity-adjusted dollars), but at a lower growth rate of 1·84% (1·68–2·02) annually, and with continuing disparities in spending between countries. In 2050, we estimate that 0·6% (0·6–0·7) of health spending will occur in currently low-income countries, despite these countries comprising an estimated 15·7% of the global population by 2050. The ratio between per capita health spending in high-income and low-income countries was 130·2 (122·9–136·9) in 2016 and is projected to remain at similar levels in 2050 (125·9 [113·7–138·1]). The decomposition analysis identified governments’ increased prioritisation of the health sector and economic development as the strongest factors associated with increases in government health spending globally. Future government health spending scenarios suggest that, with greater prioritisation of the health sector and increased government spending, health spending per capita could more than double, with greater impacts in countries that currently have the lowest levels of government health spending. Interpretation: Financing for global health has increased steadily over the past two decades and is projected to continue increasing in the future, although at a slower pace of growth and with persistent disparities in per-capita health spending between countries. Out-of-pocket spending is projected to remain substantial outside of high-income countries. Many low-income countries are expected to remain dependent on development assistance, although with greater government spending, larger investments in health are feasible. In the absence of sustained new investments in health, increasing efficiency in health spending is essential to meet global health targets. Funding: Bill & Melinda Gates Foundation

Past, present, and future of global health financing : a review of development assistance, government, out-of-pocket, and other private spending on health for 195 countries, 1995-2050

Background Comprehensive and comparable estimates of health spending in each country are a key input for health policy and planning, and are necessary to support the achievement of national and international health goals. Previous studies have tracked past and projected future health spending until 2040 and shown that, with economic development, countries tend to spend more on health per capita, with a decreasing share of spending from development assistance and out-of-pocket sources. We aimed to characterise the past, present, and predicted future of global health spending, with an emphasis on equity in spending across countries. Methods We estimated domestic health spending for 195 countries and territories from 1995 to 2016, split into three categories-government, out-of-pocket, and prepaid private health spending-and estimated development assistance for health (DAH) from 1990 to 2018. We estimated future scenarios of health spending using an ensemble of linear mixed-effects models with time series specifications to project domestic health spending from 2017 through 2050 and DAH from 2019 through 2050. Data were extracted from a broad set of sources tracking health spending and revenue, and were standardised and converted to inflation-adjusted 2018 US dollars. Incomplete or low-quality data were modelled and uncertainty was estimated, leading to a complete data series of total, government, prepaid private, and out-of-pocket health spending, and DAH. Estimates are reported in 2018 US dollars, 2018 purchasing-power parity-adjusted dollars, and as a percentage of gross domestic product. We used demographic decomposition methods to assess a set of factors associated with changes in government health spending between 1995 and 2016 and to examine evidence to support the theory of the health financing transition. We projected two alternative future scenarios based on higher government health spending to assess the potential ability of governments to generate more resources for health. Findings Between 1995 and 2016, health spending grew at a rate of 4.00% (95% uncertainty interval 3.89-4.12) annually, although it grew slower in per capita terms (2.72% [2.61-2.84]) and increased by less than $1 per capita over this period in 22 of 195 countries. The highest annual growth rates in per capita health spending were observed in upper-middle-income countries (5.55$ 8.0 trillion (7.8-8.1) in 2016 (comprising 8.6% [8.4-8.7] of the global economy and $10.3 trillion [10.1-10.6] in purchasing-power parity-adjusted dollars), with a per capita spending of US$ 5252 (5184-5319) in high-income countries, $491 (461-524) in upper-middle-income countries,$ 81 (74-89) in lower-middle-income countries, and $40 (38-43) in low-income countries. In 2016, 0.4$ 9.5 billion, 24.3% of total DAH), although spending on other infectious diseases (excluding tuberculosis and malaria) grew fastest from 2010 to 2018 (6.27% per year). The leading sources of DAH were the USA and private philanthropy (excluding corporate donations and the Bill & Melinda Gates Foundation). For the first time, we included estimates of China's contribution to DAH ($644.7 million in 2018). Globally, health spending is projected to increase to$ 15.0 trillion (14.0-16.0) by 2050 (reaching 9.4% [7.6-11.3] of the global economy and $ 21.3 trillion [19.8-23.1] in purchasing-power parity-adjusted dollars), but at a lower growth rate of 1.84% (1.68-2.02) annually, and with continuing disparities in spending between countries. In 2050, we estimate that 0.6% (0.6-0.7) of health spending will occur in currently low-income countries, despite these countries comprising an estimated 15.7% of the global population by 2050. The ratio between per capita health spending in high-income and low-income countries was 130.2 (122.9-136.9) in 2016 and is projected to remain at similar levels in 2050 (125.9 [113.7-138.1]). The decomposition analysis identified governments' increased prioritisation of the health sector and economic development as the strongest factors associated with increases in government health spending globally. Future government health spending scenarios suggest that, with greater prioritisation of the health sector and increased government spending, health spending per capita could more than double, with greater impacts in countries that currently have the lowest levels of government health spending. Interpretation Financing for global health has increased steadily over the past two decades and is projected to continue increasing in the future, although at a slower pace of growth and with persistent disparities in per-capita health spending between countries. Out-of-pocket spending is projected to remain substantial outside of high-income countries. Many low-income countries are expected to remain dependent on development assistance, although with greater government spending, larger investments in health are feasible. In the absence of sustained new investments in health, increasing efficiency in health spending is essential to meet global health targets.Peer reviewe

Past, present, and future of global health financing: a review of development assistance, government, out-of-pocket, and other private spending on health for 195 countries, 1995–2050

Background: Comprehensive and comparable estimates of health spending in each country are a key input for health policy and planning, and are necessary to support the achievement of national and international health goals. Previous studies have tracked past and projected future health spending until 2040 and shown that, with economic development, countries tend to spend more on health per capita, with a decreasing share of spending from development assistance and out-of-pocket sources. We aimed to characterise the past, present, and predicted future of global health spending, with an emphasis on equity in spending across countries. Methods: We estimated domestic health spending for 195 countries and territories from 1995 to 2016, split into three categories—government, out-of-pocket, and prepaid private health spending—and estimated development assistance for health (DAH) from 1990 to 2018. We estimated future scenarios of health spending using an ensemble of linear mixed-effects models with time series specifications to project domestic health spending from 2017 through 2050 and DAH from 2019 through 2050. Data were extracted from a broad set of sources tracking health spending and revenue, and were standardised and converted to inflation-adjusted 2018 US dollars. Incomplete or low-quality data were modelled and uncertainty was estimated, leading to a complete data series of total, government, prepaid private, and out-of-pocket health spending, and DAH. Estimates are reported in 2018 US dollars, 2018 purchasing-power parity-adjusted dollars, and as a percentage of gross domestic product. We used demographic decomposition methods to assess a set of factors associated with changes in government health spending between 1995 and 2016 and to examine evidence to support the theory of the health financing transition. We projected two alternative future scenarios based on higher government health spending to assess the potential ability of governments to generate more resources for health. Findings: Between 1995 and 2016, health spending grew at a rate of 4·00% (95% uncertainty interval 3·89–4·12) annually, although it grew slower in per capita terms (2·72% [2·61–2·84]) and increased by less than $1 per capita over this period in 22 of 195 countries. The highest annual growth rates in per capita health spending were observed in upper-middle-income countries (5·55 in lower-middle-income countries (3·71$8·0 trillion (7·8–8·1) in 2016 (comprising 8·6% [8·4–8·7] of the global economy and $10·3 trillion [10·1–10·6] in purchasing-power parity-adjusted dollars), with a per capita spending of US$5252 (5184–5319) in high-income countries, $491 (461–524) in upper-middle-income countries,$81 (74–89) in lower-middle-income countries, and $40 (38–43) in low-income countries. In 2016, 0·4 countries, despite these countries comprising 10·0 DAH targeted HIV/AIDS ($9·5 billion, 24·3% of total DAH), although spending on other infectious diseases (excluding tuberculosis and malaria) grew fastest from 2010 to 2018 (6·27% per year). The leading sources of DAH were the USA and private philanthropy (excluding corporate donations and the Bill & Melinda Gates Foundation). For the first time, we included estimates of China’s contribution to DAH ($644·7 million in 2018). Globally, health spending is projected to increase to$15·0 trillion (14·0–16·0) by 2050 (reaching 9·4% [7·6–11·3] of the global economy and $21·3 trillion [19·8–23·1] in purchasing-power parity-adjusted dollars), but at a lower growth rate of 1·84% (1·68–2·02) annually, and with continuing disparities in spending between countries. In 2050, we estimate that 0·6% (0·6–0·7) of health spending will occur in currently low-income countries, despite these countries comprising an estimated 15·7% of the global population by 2050. The ratio between per capita health spending in high-income and low-income countries was 130·2 (122·9–136·9) in 2016 and is projected to remain at similar levels in 2050 (125·9 [113·7–138·1]). The decomposition analysis identified governments’ increased prioritisation of the health sector and economic development as the strongest factors associated with increases in government health spending globally. Future government health spending scenarios suggest that, with greater prioritisation of the health sector and increased government spending, health spending per capita could more than double, with greater impacts in countries that currently have the lowest levels of government health spending Interpretation: Financing for global health has increased steadily over the past two decades and is projected to continue increasing in the future, although at a slower pace of growth and with persistent disparities in per-capita health spending between countries. Out-of-pocket spending is projected to remain substantial outside of high-income countries. Many low-income countries are expected to remain dependent on development assistance, although with greater government spending, larger investments in health are feasible. In the absence of sustained new investments in health, increasing efficiency in health spending is essential to meet global health targets. Funding: Bill & Melinda Gates Foundatio