added nesterov momentum method

src/shogun/optimization/NesterovMomentumCorrection.h

@@ -0,0 +1,101 @@
+/*
+ * Copyright (c) The Shogun Machine Learning Toolbox
+ * Written (w) 2015 Wu Lin
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright notice, this
+ *    list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright notice,
+ *    this list of conditions and the following disclaimer in the documentation
+ *    and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
+ * WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+ * DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
+ * ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
+ * (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+ * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
+ * ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ *
+ * The views and conclusions contained in the software and documentation are those
+ * of the authors and should not be interpreted as representing official policies,
+ * either expressed or implied, of the Shogun Development Team.
+ *
+ */
+
+#ifndef NESTEROVMOMENTUMCORRECTION_H
+#define NESTEROVMOMENTUMCORRECTION_H
+#include <shogun/lib/config.h>
+#include <shogun/optimization/MomentumCorrection.h>
+namespace shogun
+{
+/** @brief This implements the Nesterov's Accelerated Gradient (NAG) correction.
+ *
+ * Given a target variable, \f$w\f$, and its gradient, \f$d\f$, the momentum method performs the following update.
+ *  \f$ w_{ahead}= w + \mu v \f$
+ *  \f$ v^{new} = \mu v - \lambda d_{ahead} \f$
+ *  \f$ w^{new} = w + v \f$
+ * where \f$mu\f$ is a momentum, \f$d_{ahead}\f$ is the gradient of \f$w_{ahead}\f$, \f$v\f$ is a previous descend direction, \f$\lambda\f$ is a learning rate, and \f$v^{new}\f$ is a corrected descend direction.
+ *
+ *  Note that the Nesterov momentum correction makes use of \f$d_{ahead}\f$  instead of the gradient of \f$w\f$, \f$d\f$.
+ *
+ * In practice, we use the following implementation:
+ * \f$ v^{old} = v \f$
+ * \f$ v^{new} = \mu  v^{old} - \lambda d \f$
+ * \f$ w^{new} = w - \mu  v^{old} + (1 + \mu) v^{new} \f$
+ * The trick used in this implementation is we store \f$w_{ahead}\f$ and rename it as \f$w\f$
+ *
+ * Given a decay learning_rate, \f$w_{ahead}$\f is very close to \f$w$\f. 
+ * When an optimal solution \f$w^{opt}\f$ is found, \f$w_{ahead}=w^{opt}$\f since \f$d^{opt}=0\f$
+ *
+ * The get_corrected_descend_direction methods will do 
+ * \f$ v^{old} = v \f$
+ * \f$ v^{new} = \mu  v^{old} - \lambda d \f$
+ * and return \f$ -\mu  v^{old} + (1 + \mu) v^{new}\f$
+ *
+ * A good introduction to the momentum update can be found at
+ * http://cs231n.github.io/neural-networks-3/#sgd
+ *
+ * If you read the introduction at http://cs231n.github.io/neural-networks-3/#sgd ,
+ * you may know that \f$v\f$ is also called velocity.
+ */
+class NesterovMomentumCorrection: public MomentumCorrection
+{
+public:
+	/*  Constructor */
+	NesterovMomentumCorrection()
+		:MomentumCorrection()
+	{
+		init();
+	}
+
+	/*  Destructor */
+	virtual ~NesterovMomentumCorrection() {}
+
+	/** Get corrected descend direction
+	 *
+	 * @param gradient gradient
+	 * @param idx the index of the direction
+	 * 
+	 * @return corrected descend direction
+	 */
+	virtual float64_t get_corrected_descend_direction(float64_t gradient, index_t idx)
+	{
+		REQUIRE(idx>=0 && idx<m_previous_descend_direction.vlen,"The index (%d) is invalid\n", idx);
+		float64_t tmp=m_weight*m_previous_descend_direction[idx];
+		m_previous_descend_direction[idx]=tmp-gradient;
+		return (1.0+m_weight)*m_previous_descend_direction[idx]-tmp;
+	}
+private:
+	/*  Init */
+	void init() { m_weight=0.9; }
+};
+
+}
+#endif