Ahead of the 21st Bafta games awards this April, the institution is running a public survey asking people to nominate the most influential video game of all time. As the survey points out, this is an open-ended question: early, groundbreaking titles such as Space Invaders and Pong regularly crop up as answers because they helped write the rules of the form, but on a personal level, the right game at the right time can be exceptionally influential, too. For players, it's often the games that made us feel differently about what games could do that feel the most influential. For a game designer, a film director, a writer or a musician, one particular game might inspire a whole creative era. Inspired by Bafta's survey, we asked people from across games and culture for their most influential game – and not one name cropped up twice.

We propose a novel method that solves global optimization problems in two steps: (1) perform a (exponential) power-$N$ transformation to the not-necessarily differentiable objective function $f$ and get $f_N$, and (2) optimize the Gaussian-smoothed $f_N$ with stochastic approximations. Under mild conditions on $f$, for any $\delta>0$, we prove that with a sufficiently large power $N_\delta$, this method converges to a solution in the $\delta$-neighborhood of $f$'s global optimum point. The convergence rate is $O(d^2\sigma^4\varepsilon^{-2})$, which is faster than both the standard and single-loop homotopy methods if $\sigma$ is pre-selected to be in $(0,1)$. In most of the experiments performed, our method produces better solutions than other algorithms that also apply smoothing techniques.

In the fifth article of this series, we will continue to summarise a collection of commonly used technical analysis trading models that will steadily increase in mathematical and computational complexity. Typically, these models are likely to be most effective around fluctuating or periodic instruments, such as forex pairs or commodities, which is what I have backtested them on. The aim behind each of these models is that they should be objective and systematic i.e. we should be able to translate them into a trading bot that will check some conditions at the start of each time period and make a decision if a buy or sell order should be posted or whether an already open trade should be closed. Please note that not all of these trading models are successful. In fact, a large number of them were unsuccessful.

We propose a Fourier-based approach for optimization of several clustering algorithms. Mathematically, clusters data can be described by a density function represented by the Dirac mixture distribution. The density function can be smoothed by applying the Fourier transform and a Gaussian filter. The determination of the optimal standard deviation of the Gaussian filter will be accomplished by the use of a convergence criterion related to the correlation between the smoothed and the original density functions. In principle, the optimal smoothed density function exhibits local maxima, which correspond to the cluster centroids. Thus, the complex task of finding the centroids of the clusters is simplified by the detection of the peaks of the smoothed density function. A multiple sliding windows procedure is used to detect the peaks. The remarkable accuracy of the proposed algorithm demonstrates its capability as a reliable general method for enhancement of the clustering performance, its global optimization and also removing the initialization problem in many clustering methods.

Minimax optimization plays a key role in adversarial training of machine learning algorithms, such as learning generative models, domain adaptation, privacy preservation, and robust learning. In this paper, we demonstrate the failure of alternating gradient descent in minimax optimization problems due to the discontinuity of solutions of the inner maximization. To address this, we propose a new epsilon-subgradient descent algorithm that addresses this problem by simultaneously tracking K candidate solutions. Practically, the algorithm can find solutions that previous saddle-point algorithms cannot find, with only a sublinear increase of complexity in K. We analyze the conditions under which the algorithm converges to the true solution in detail. A significant improvement in stability and convergence speed of the algorithm is observed in simple representative problems, GAN training, and domain-adaptation problems.