We propose a network architecture which uses a single internal layer of locally-tuned processing units to learn both classification tasks and real-valued function approximations (Moody and Darken 1988). We consider training such networks in a completely supervised manner, but abandon this approach in favor of a more computationally efficient hybrid learning method which combines self-organized and supervised learning. Our networks learn faster than backpropagation for two reasons: the local representations ensure that only a few units respond to any given input, thus reducing computational overhead, and the hybrid learning rules are linear rather than nonlinear, thus leading to faster convergence. Unlike many existing methods for data analysis, our network architecture and learning rules are truly adaptive and are thus appropriate for real-time use.

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We present methods for optimizing portfolios, asset allocations, and trading systems based on direct reinforcement (DR). In this approach, investment decision-making is viewed as a stochastic control problem, and strategies are discovered directly. We present an adaptive algorithm called recurrent reinforcement learning (RRL) for discovering investment policies. The need to build forecasting models is eliminated, and better trading performance is obtained. The direct reinforcement approach differs from dynamic programming and reinforcement algorithms such as TD-learning and Q-learning, which attempt to estimate a value function for the control problem. We find that the RRL direct reinforcement framework enables a simpler problem representation, avoids Bellman's curse of dimensionality and offers compelling advantages in efficiency. We demonstrate how direct reinforcement can be used to optimize risk-adjusted investment returns (including the differential Sharpe ratio), while accounting for the effects of transaction costs. In extensive simulation work using real financial data, we find that our approach based on RRL produces better trading strategies than systems utilizing Q-learning (a value function method). Real-world applications include an intra-daily currency trader and a monthly asset allocation system for the S&P 500 Stock Index and T-Bills.

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We propose to train trading systems and portfolios by optimizing objective functions that directly measure trading and investment performance. Rather than basing a trading system on forecasts or training via a supervised learning algorithm using labelled trading data, we train our systems using recurrent reinforcement learning (RRL) algorithms. The performance functions that we consider for reinforcement learning are profit or wealth, economic utility, the Sharpe ratio and our proposed differential Sharpe ratio. The trading and portfolio management systems require prior decisions as input in order to properly take into account the effects of transactions costs, market impact, and taxes. This temporal dependence on system state requires the use of reinforcement versions of standard recurrent learning algorithms. We present empirical results in controlled experiments that demonstrate the efficacy of some of our methods for optimizing trading systems and portfolios. For a long/short trader, we find that maximizing the differential Sharpe ratio yields more consistent results than maximizing profits, and that both methods outperform a trading system based on forecasts that minimize MSE. We find that portfolio traders trained to maximize the differential Sharpe ratio achieve better risk‐adjusted returns than those trained to maximize profit. Finally, we provide simulation results for an S&P 500/TBill asset allocation system that demonstrate the presence of out‐of‐sample predictability in the monthly S&P 500 stock index for the 25 year period 1970 through 1994. Copyright © 1998 John Wiley & Sons, Ltd.