# A Sarsa based Autonomous Stock Trading Agent

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3 Price Rising Price Figure 2: A rising price market condition with stock price rising during the day A rising price is generated as follows to ensure that the price doesn t grow exponentially during any trading day but at the same time remained random. a = Random Number; if (a <.1) { Base Price = Base Price + a *.1 * Base Price; } return Base Price + a *.1 * Base Price; Price Falling Price Figure 3: A falling price market condition with stock price falling during the day The falling price can be generated similarly by ensuring that the price is decreased fractionally at random intervals. The price of the stock is independent of the trading behavior of the agents participating in the markets and is completely determined by the combination of market conditions used during any given trading day. This separation of stock price from the trading activity of the agents enabled the Sarsa agent to focus entirely on making the optimal trading decision without having to model the behavior of other agents and the effect of their behavior on the stock price. This model is also a close approximation of the environment in which small volume traders operate on a real electronic market where their actions have almost no direct effect on the price of the stock.

4 Price Mixed Price Figure 4: A mixed price market condition with stock price rising in the first half of the day and falling during the rest of the day 3 The Sarsa λ based Agent The Sarsa [1] algorithm is an On-Policy algorithm for TD-Learning. The major difference between it and Q-Learning [7] is that the maximum reward for the next state is not necessarily used for updating the Q-values. Instead, a new action, and therefore reward, is selected using the same policy that determined the original action. The name Sarsa actually comes from the fact that the updates are done using the quintuple Q(s, a, r, s', a'). Where: s, a are the original state and action, r is the reward observed in the following state and s', a' are the new state-action pair. The Stock trading agent uses Sarsa algorithm because it incorporates the cost of exploration into the estimated Q values and therefore learns the best possible policy given the current rate of exploration while Q-Learning would learn the optimal policy when there is no exploration but may not find the policy that would provide maximum reward given the current rate of exploration. The autonomous stock trading agent operates in non-stationary environment and it is necessary to continue to explore and learn throughout its operation and Sarsa algorithm ensures that agents learns the policy that would give maximum reward possible with the current rate of exploration. 3.1 The Agent Specification In its basic form, a reinforcement learning problem is given by a 4-tuple {S,A,T,R}, where S is a finite set of the environment s states; A is a finite set of actions available to the agent as a means of extracting an economic benefit from the environment, referred to as reward, and possibly of altering the environment state; T : S A S is a state transition function; and R : S A R is a reward function. The state transition and reward functions T and R are possibly stochastic and unknown to the agent. The objective is to develop a policy, i.e., a mapping from environment states to actions, which maximizes the long-term return. A common definition of return, and one used in this agent, is the discounted sum of rewards: t= γ t r t where < γ < 1 is a discount factor and r t is the reward received at time t. State space. The state of the environment is observed by the stock trading agent through the price of the stock. The deviation of the current price from the estimated real value of

9 Figures 9, 1, 11 and 12 compares the performance of Sarsa-trader with the hand coded agent during steady price, rising price, falling price and mixed price market conditions. The graphs show that Sarsa-agent outperforms the hand coded agent in each of the market conditions with a significant margin. The graphs also indicate that profits earned by both the agents are steadily rising over the trading period without big fluctuations. This is partly because the price movements used the market stimulator are minor and doesn t include any drastic rise or fall in prices. TotalAsset RL TradeAganistTrend Figure 1: Performance of the agents in a rising price market condition TotalAsset RL TradeAganistTrend Figure 11: Performance of the agents in a falling price market condition Price RL TradeAganistTrend Figure 12: Performance of the agents in a mixed price market condition

11 7 Acknowledgements I thank Professor Peter Stone for his guidance during the project and also actively sharing his expertise in reinforcement learning theory through his lectures, assignments, reviews and discussions. References [1] R.S. Sutton and A.G. Barto, Reinforcement Learning: An Introduction, MIT Press, [2] Sherstov, A. and Stone, P. 24. Three Automated Stock-Trading Agents: A Comparative Study. In AAMAS 24 Workshop on Agent Mediated Electronic Commerce VI. [3] Feng, Y., Yu, R. and Stone, P. 24. Two Stock-Trading Agents: Market Making and Technical Analysis. In Agent Mediated Electronic Commerce V, Lecture Notes in Artificial Intelligence, pp , Springer Verlag. [4] Moody, J. and Saffell, M. 21. Learning to trade via direct reinforcement. IEEE Trans. Neural Networks 12(4): [5] Dempster, M.A.H. and Jones, C.M. 21. A real-time adaptive trading system using genetic programming. Quantitative Finance 1: [6] Singh, S.P., Sutton, R.S. (1996). Reinforcement learning with replacing eligibility traces. Machine Learning 22(1/2/3): [7] Watkins, C. J. C. H. and Dayan, P Q-learning. Machine Learning 8(3):

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