Random Search Algorithms for Optimal Control

Joose Rajamäki

Random Search Algorithms for Optimal Control

Julkaisun otsikon käännös: Satunnaishakualgoritmeja optimaaliseen säätöön

Joose Rajamäki

Tutkimustuotos: Doctoral Thesis › Collection of Articles

Abstrakti

Optimisäätö on tärkeä väline useilla sovellusalueilla, se on esimerkiksi keskeinen työkalu robotiikassa. Monet laajasti käytössä olevat menetelmät kuten differentiaalinen dynaaminen optimointi (DDP) perustuvat ohjatun järjestelmän dynamiikan ja kohdefunktion differentiointiin. Oletus järjestelmän mallin differentioituvuudesta ei päde monille järjestelmille, joita halutaan säätää. Esimerkiksi törmäykset rikkovat kyseisen olettaman. Tässä tapauksessa on otettava käyttöön satunnaishaku- eli Monte Carlo algoritmit. Tässä väitöskirjassa esitetyt satunnaishakualgoritmit jakautuvat kahteen kategoriaan. Toinen näistä on lokaalisti optimaaliset satunnaishakuun perustuvat liikerataoptimointimenetelmät. Toinen kategorioista on reaaliaikaiseen ohjaukseen kykenevät Monte Carlo puuhakumenetelmät (MCTS), joita on täydennetty koneoppimismenetelmillä, joita koulutetaan valvotulla oppimisella. Tämä väitöskirja esittää näytteistetyn differentiaalisen dynaamisen optimoinnin (SaDDP), joka on differentiaalisesta dynaamisesta optimoinnista johdettu satunnaishakuun perustuva liikerataoptimointimenetelmä. SaDDP on johdettu rinnastamalla DDP:ssä käytetyn Taylor-kehitelmän suureet moniulotteisen normaalijakauman tunnuslukuihin. Nämä tunnusluvut voidaan laskea uudelleen näytteistä sen sijaan, että käytettäisiin differentiointia niiden laskemiseen. Tämä väitöskirja esittää myös tapoja SaDDP:n tehokkaaseen regularisoimiseen. Tässä väitöskirjassa esitetyt reaaliaikaiseen säätöön kykenevät MCTS-menetelmät mahdollistavat monimutkaisten järjestelmien, kuten 3D-hahmojen, ohjaamisen. Menetelmät suorittavat loitontuvan horisontin haun ja käyttävät haun tuottamaa dataa koneoppimismallien opettamiseen. Nämä koneoppimismallit vuorostaan avustavat tulevia hakuja. Kyseinen loitontuvan horisontin haku yhdistettynä valvottuun koneoppimiseen konvergoi nopeasti ja saa algoritmin oppimaan vakaasti. Tämän väitöskirjan MCTS-menetelmät yhdistävät informaatiota useista lähteistä. Tässä väitöskirjassa esitetään, miten näiden lähteiden sisältämä informaatio voidaan yhdistää siten, että menetelmä sopeutuu tilanteisiin, jossa informaatio on yhtenevää taikka ristiriitaista. Näiden uudenlaisten hakualgoritmien lisäksi tässä väitöskirjassa esitetään MCTS-haku, jota avustaa generatiivinen neuroverkko. Tämä yhdistelmä mahdollistaa sen, että neuroverkko voi oppia suorittamaan useita vaihtoehtoisia toimintoja kussakin tilassa.

Julkaisun otsikon käännös	Satunnaishakualgoritmeja optimaaliseen säätöön
Alkuperäiskieli	Englanti
Pätevyys	Tohtorintutkinto
Myöntävä instituutio	Aalto-yliopisto
Valvoja/neuvonantaja	Hämäläinen, Perttu, Vastuuprofessori Hämäläinen, Perttu, Ohjaaja Kyrki, Ville, Ohjaaja
Kustantaja	Aalto University
Painoksen ISBN	978-952-60-8155-7
Sähköinen ISBN	978-952-60-8156-4
Tila	Julkaistu - 2018
OKM-julkaisutyyppi	G5 Artikkeliväitöskirja

Tutkimusalat

Monte Carlo -puuhaku
differentiaalinen dynaaminen optimointi

Pääsy asiakirjaan

http://urn.fi/URN:ISBN:978-952-60-8156-4Lisenssi: Määrittelemätön

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@phdthesis{296419563b234b649bee99ba18833a48,

title = "Random Search Algorithms for Optimal Control",

abstract = "Optimal control is an important tool in many application areas, it is for example a central tool in robotics. Many widely used methods such as differential dynamic programming (DDP) are based on differentiating the dynamics of the controlled systems and the objective function. The assumption that one would have access to a differentiable model of the entire system does not hold for many systems of interest. For example, collisions break this assumption. In this case one has to resort to random search (Monte Carlo) algorithms. This thesis presents random search algorithms that fall into two categories. The first category is locally optimal sampling based trajectory optimization methods. The second one is real-time capable Monte Carlo tree search (MCTS) methods augmented with supervised machine learning. This thesis presents sampled differential dynamic programming (SaDDP), which is a random search trajectory optimization method, derived from the differential dynamic programming algorithm. SaDDP is derived by relating the quantities of the Taylor-expansion in DDP to the statistics of a multivariate normal distribution. This allows the statistics to be recomputed from sampled data instead of utilizing differentiation to obtain them. The thesis also presents ways to regularize the SaDDP algorithm efficiently. The real-time capable MCTS methods presented in this thesis enable the real-time control of complicated systems, such as physics-based 3D characters. The methods perform a receding horizon lookahead search and use the data produced by the lookahead search to teach machine learning models how to better search for the actions in the future. The demonstrated combination of receding horizon search and supervised learning is fast to converge and yields robust learning. The MCTS in this thesis combines information from multiple sources. This thesis presents how to combine the information from various sources in such a way that the search adapts to the information sources agreeing or disagreeing. In addition to new search algorithms, this thesis presents a combination of MCTS and a neural network generative model. This combination enables the neural network to learn that it can perform different actions in a single state.",

keywords = "Monte Carlo, Monte Carlo tree search, differential dynamic programming, Monte Carlo -puuhaku, differentiaalinen dynaaminen optimointi, Monte Carlo, Monte Carlo tree search, differential dynamic programming",

author = "Joose Rajam{\"a}ki",

year = "2018",

language = "English",

isbn = "978-952-60-8155-7",

series = "Aalto University publication series DOCTORAL DISSERTATIONS",

publisher = "Aalto University",

number = "164",

address = "Finland",

school = "Aalto University",

}

TY - BOOK

T1 - Random Search Algorithms for Optimal Control

AU - Rajamäki, Joose

PY - 2018

Y1 - 2018

N2 - Optimal control is an important tool in many application areas, it is for example a central tool in robotics. Many widely used methods such as differential dynamic programming (DDP) are based on differentiating the dynamics of the controlled systems and the objective function. The assumption that one would have access to a differentiable model of the entire system does not hold for many systems of interest. For example, collisions break this assumption. In this case one has to resort to random search (Monte Carlo) algorithms. This thesis presents random search algorithms that fall into two categories. The first category is locally optimal sampling based trajectory optimization methods. The second one is real-time capable Monte Carlo tree search (MCTS) methods augmented with supervised machine learning. This thesis presents sampled differential dynamic programming (SaDDP), which is a random search trajectory optimization method, derived from the differential dynamic programming algorithm. SaDDP is derived by relating the quantities of the Taylor-expansion in DDP to the statistics of a multivariate normal distribution. This allows the statistics to be recomputed from sampled data instead of utilizing differentiation to obtain them. The thesis also presents ways to regularize the SaDDP algorithm efficiently. The real-time capable MCTS methods presented in this thesis enable the real-time control of complicated systems, such as physics-based 3D characters. The methods perform a receding horizon lookahead search and use the data produced by the lookahead search to teach machine learning models how to better search for the actions in the future. The demonstrated combination of receding horizon search and supervised learning is fast to converge and yields robust learning. The MCTS in this thesis combines information from multiple sources. This thesis presents how to combine the information from various sources in such a way that the search adapts to the information sources agreeing or disagreeing. In addition to new search algorithms, this thesis presents a combination of MCTS and a neural network generative model. This combination enables the neural network to learn that it can perform different actions in a single state.

AB - Optimal control is an important tool in many application areas, it is for example a central tool in robotics. Many widely used methods such as differential dynamic programming (DDP) are based on differentiating the dynamics of the controlled systems and the objective function. The assumption that one would have access to a differentiable model of the entire system does not hold for many systems of interest. For example, collisions break this assumption. In this case one has to resort to random search (Monte Carlo) algorithms. This thesis presents random search algorithms that fall into two categories. The first category is locally optimal sampling based trajectory optimization methods. The second one is real-time capable Monte Carlo tree search (MCTS) methods augmented with supervised machine learning. This thesis presents sampled differential dynamic programming (SaDDP), which is a random search trajectory optimization method, derived from the differential dynamic programming algorithm. SaDDP is derived by relating the quantities of the Taylor-expansion in DDP to the statistics of a multivariate normal distribution. This allows the statistics to be recomputed from sampled data instead of utilizing differentiation to obtain them. The thesis also presents ways to regularize the SaDDP algorithm efficiently. The real-time capable MCTS methods presented in this thesis enable the real-time control of complicated systems, such as physics-based 3D characters. The methods perform a receding horizon lookahead search and use the data produced by the lookahead search to teach machine learning models how to better search for the actions in the future. The demonstrated combination of receding horizon search and supervised learning is fast to converge and yields robust learning. The MCTS in this thesis combines information from multiple sources. This thesis presents how to combine the information from various sources in such a way that the search adapts to the information sources agreeing or disagreeing. In addition to new search algorithms, this thesis presents a combination of MCTS and a neural network generative model. This combination enables the neural network to learn that it can perform different actions in a single state.

KW - Monte Carlo

KW - Monte Carlo tree search

KW - differential dynamic programming

KW - Monte Carlo -puuhaku

KW - differentiaalinen dynaaminen optimointi

KW - Monte Carlo

KW - Monte Carlo tree search

KW - differential dynamic programming

M3 - Doctoral Thesis

SN - 978-952-60-8155-7

T3 - Aalto University publication series DOCTORAL DISSERTATIONS

PB - Aalto University

ER -

Random Search Algorithms for Optimal Control

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