# Asynchronously solving problems with privacy requirements

### School

Swiss Federal Institute of Technology (EPFL)

### Supervisors

Boi Faltings

### Abstract

Asynchronous search techniques for distributed satisfaction problems
are among the scientific challenges of Distributed Artificial
Intelligence. They are useful in applications like negotiations
(Generalized English Auctions), distributed meeting scheduling with
private constraints, distributed configuration with secret know-how.
Asynchronous search also has an important theoretic value, defining
generic techniques whose properties, once
proven, apply to a large number of not only distributed but also
centralized old and new algorithms. A convincing example is the technique I
propose for using backtracking nogoods in consistency
(Section~\ref{sec:AMC:dmac-abt}), technique that can be
straightforwardly applied to classic centralized versions of backtracking (as
I show in Section~\ref{sec:DPF:FBT}) with improvements of
efficiency.
Despite the continuous effort of the last ten years, several important
issues remained open until now. This thesis describes several
advances that allow the agents to get more opportunities to
communicate. It also proposes new frameworks for
distributed constraint satisfaction, and strategies for agents. The
main focus is on asynchronous complete search with polynomial space
requirements in the size of the global problem, where the global
problem is distributed naturally.
Among the main contributions I mention:
* Local consistency is a technique bringing gains that are exponential
in the size of the problem, by deposing an effort that is exponential
in the size of the used predicates (constraints). The effort can
therefore be polynomial in the size of the global problem. {\bf Exponential
gain with polynomial cost} made local consistency the most important
technique in constraint satisfaction where it was shown that any
opportunity must be used for exploiting it ({\em
consistency maintenance}). I generalize the concept of centralized
consistency maintenance in a way that makes it applicable to
asynchronous techniques. This is the first technique allowing for
consistency maintenance in asynchronous search and is very efficient (Chapter~\ref{chap:AMC}).
* I noticed that the use of CSPs techniques for numeric problems over
\R{} was possible by something that can be described as: {\em letting
the domain splits have existential meaning rather than the universal
meaning in classical backtracking}. Existing asynchronous search
protocols supported only proposals with universal quantifiers
(e.g. {\bf require}($\forall x\in\{1\})$). I modify and generalize
existing asynchronous search protocols to support proposals with
existential quantifiers (e.g. {\bf require}($\exists
x\in\{[1.5,10^5]\cup\{0,1\}\}$)). This efficient technique is the
first to allow a {\bf proper use of intervals} in proposals and is
a first step I took for extending the applicability of asynchronous
search to Numeric CSPs. Since this idea came when I tried to integrate
in ABT an aggregation technique described in~\cite{rfia00}, the
first protocol with the desired property is called Asynchronous
Aggregation Search (see Chapter~\ref{chap:AAS}).
* Existing algorithms enforced a static priority
on agents. This is a drawback. It entangles agents to {\em verify
conflicts in Generalized English Auctions} (Chapter~\ref{chap:ASS}), for
defending themselves from unfair competition. One only knew to remove
that constraint at the expense of requiring an unbounded computer
memory (e.g. RAM). This is infeasible and leads to unwarranted
protocols. I designed the first solving protocol that {\bf allows the
needed dynamic reordering} and still has {\bf a guaranteed
termination} with polynomially bounded computer space
requirements. Moreover, the designed technique is very general as
it can introduce all important reordering heuristics used for
efficiency in centralized techniques (see Chapter~\ref{chap:ABTR}).
* Besides the aforementioned reordering technique, I propose a suite of
other techniques for dynamic reordering with other types of
heuristics and still offering guaranteed termination with polynomial
space requirements: Reordering with increasing delay restarts
(Section~\ref{sec:ABTR:restarts}), and Finite number of
reorderings. These two techniques are simple but allow only simplistic
reordering heuristics. Dynamic Partial Order is discussed in
Section~\ref{sec:ABTR:poas}.
* Proposals with existential quantifiers are not sufficient for enabling
application of search to numeric problems. The remaining requirement
is that {\em proposals must not be binding}. Actually, one of the powerful
and general available centralized techniques for solving numeric
problems is the one proposed in Section~\ref{sec:cDPF:uca6}. Domains
are split recursively, and {\bf the same constraints are recursively
reverified} until complete satisfaction or an acceptable resolution is
obtained.
* Asynchronous techniques requested an agent only once its proposal. The
proposals were therefore necessarily binding. This is incompatible
with the practice required for numeric problems, as mentioned at the
previous item. After understanding this problem, I proposed a
modeling technique called Replica-based search. Several replicas
of the same agent are asked proposals at different levels of
abstractions. As a result, {\bf proposals of the replicas are not
binding}. They can be refused by subsequent replicas (e.g. After an
agent sends {\bf require}($\exists x\in\{[1.5,10^5]\cup\{0,1\}\}$), it
can be more restrictive in a subsequent replica, {\bf
require}($\exists x\in\{[15,1000]\}$), and later can even abandon
completely its proposal, {\bf
require}($x\not\in\{[1.5,10^5]\cup\{0,1\}\}$)). This technique,
described in Chapter~\ref{chap:RDisCSP} closes the sequence of ideas
required for developing asynchronous techniques for numeric problems
over \R.
* One of the main motivations for distributed algorithms is the
enforcement of privacy. A framework for modeling and quantifying
privacy loss and a {\bf theoretic comparison on the power of different
protocols in saving privacy} are proposed in
Chapter~\ref{chap:Privacy}.
* Hewlett-Packard, learning that the ink-jet printer is a competitor for
their main product, the laser printer, decided to also develop ink-jet
printers in parallel. With the same principle in mind, I developed and
analyzed an expensive secure protocol (SCSPS), proposed in
Chapter~\ref{chap:Secure}. I also developed and analyzed {a set of
cryptographic protocols for both discrete and numeric distributed
satisfaction problems} (Annex~\ref{chap:Test}). For the work described
in Annex~\ref{chap:Test}, another important contribution
is the discovery of the
feebleness of that type of techniques, the ``S-attacks''.
The obtained cryptographic protocols have some drawbacks such that a
trade-off remains between the competing techniques. Secure protocols
and distributed algorithms will continue to coexist for a while, as
laser printers and ink-jet printers.
* Several distributed optimization techniques have been developed so far. Those
techniques are not general and abstract enough for allowing extensions
like consistency maintenance and reordering. The notion of cost was
unclear. I {\bf introduce the notion of cost in nogoods, obtaining a
general stand-alone communication atom}. In
Chapter~\ref{chap:Optimization} I describe a generalization of all the
existing distributed satisfaction and optimization techniques. This
generalization allows the introduction of consistency maintenance,
reordering, etc. in distributed optimization.
* Negotiations are defined by the fact that the participants yield from
their constraints to reach common solutions. This is technically
called: constraint relaxation. No relaxation technique existed for private
problems. I propose such a technique for private constraints
(Section~\ref{sec:GEA:CR}). A classical dualism for CSPs defines a
standard transfer between privacy on constraints and privacy on
domains (see Section~\ref{sec:domain-constraints} and
Chapter~\ref{chap:DisGCSP}). We have also defined a primal version of
this technique.
SNEAKERS