1. Evolving Trading Ruleswith XCSF Daniele Loiacono Artificial Intelligence and Robotics Laboratory,Politecnico di Milano, Italy GECCO'07, July 7-11, 2007, London, UK.

2. Outline

Introduction to XCSF

The framework

Experimental results

Conclusions

3. What is a learning classifier system?

M achine learning paradigm

Solves problemsevolvinga set ofrules(the classifiers)

Theknowledgeis thus represented with apopulationof rules

In stateS,doing actionAwill resultin a payoffP , estimated with accuracyF

4. XCSF

Introduced by Wilson in 2001

The classifier payoff P iscomputed by a parameterized function p(S, w )

Overall XCSF consists of

• Reinforcement Learning techniques to build the payoff target (prediction)P = p(S,w)

• Gradient descent to learn the parametersw

• A genetic algorithm, based on accuracy, as generalization mechanism

5. Outline

Introduction to XCSF

The framework

Experimental results

Conclusions

6. The Framework STOCK10 VolumePrice STOCK1 VolumePrice STOCK2 VolumePrice INPUT ? SYSTEM Buy/Sell transactions for earning a lot of $$$ 7. Problem Decomposition STOCK10 VolumePrice STOCK1 VolumePrice STOCK2 VolumePrice INPUT Buy/Sell transactions for earning a lot of $$$STOCK1 Expert STOCK2 Expert STOCK3 Expert Merge Expert 8. The stock experts INPUT BUY HOLD SELL Action Suggested FEATURE EXTRACTION AND NORMALIZATION EXPERT KB EVOLVED WITH XCSF 9. Feature Extraction

The known indicators are an obvious choice

We used three well know indicators:

• PPO (12,26,9) for the stock price

• RSI with period 14 for the stock price

• PPO (12,26,9)for the stock volume

In addition we also used as feature the fraction of the overall portfolio value invested in the stock

Finally features are normalized between -1 and 1

10. Evolving the KB

The KB is a set of rules evolved with XCSF applied to a single stock portfolio optimization problem.

At each time step XCSF can:

• buy a fixed amount of shares of the stock

• sell a fixed amount of shares of the stock

• hold the current position

Goal is maximizing the income over time

11. Merging Expert

We merged all the stock expert suggestions with a simple heuristic algorithm

First an exponential moving average of each stock suggestions is computed (a numerical value is associated to buy, hold and sell)

For each stock with an average suggestion of selling higher than a threshold, a fixed amount of shares is sold

For each stock with an average suggestion of buying higher than a threshold, a fixed amount of shares is bought

12. Outline

Introduction to XCSF

The framework

Experimental results

Conclusions

13. Experimental setup

The data set provided for the competition was partitioned in two set: a training set (900 samples) and a validation set (246 samples)

XCSF was applied on the training set for evolving the KB of the 10 stock experts

A 10-fold crossvalidation was used for tuning XCSF parameters

Finally the overall system (the 10 stock experts and the merge one) was tested on the validation set

14. Validation results 15. Test Results

The system was finally tested on a the official test set provided for the competition

16. Outline

Introduction to XCSF

The framework

Experimental results

Conclusions

17. Discussion of results

Why so a different performance on different dataset ?

Financial market are complex

But have a look to the dataset:

TRAININGSET 18. Discussion of results

Why so a different performance on different dataset ?

Financial market are complex

But have a look to the dataset:

VALIDATION SET 19. Discussion of results

Why so a different performance on different dataset ?

Financial market are complex

But have a look to the dataset:

TESTSET 20. Conclusions

We introduced a very simple framework for evolving trading rules with XCSF

Results are mixed and further investigation is necessary for a better understanding and improvements of the system performance

There are a lot of possible extensions:

• Choice of technical indicators

• Evolving the merge expert