Brendan Juba MIT CSAIL amp Harvard w ith Madhu Sudan MSR amp MIT Motivation Beliefs model Sketch of result 2 Miscommunication happens Got that Q CAN COMPUTERS COPE WITH MISCOMMUNICATION AUTOMATICALLY ID: 189780
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Slide1
Efficient Semantic Communication via Compatible Beliefs
Brendan Juba
(MIT CSAIL & Harvard)
w
ith
Madhu
Sudan (MSR & MIT)Slide2
Motivation
Beliefs model
Sketch of result
2Slide3
Miscommunication happens…
Got that?
Q:
CAN COMPUTERS COPE
WITH MISCOMMUNICATION AUTOMATICALLY??
3Slide4
Printer
Defining (
mis
)communication
Printer driver
Printer firmware
ENVIRONMENT
INTERFACE FIXED IN ADVANCE
4Slide5
ENVIRONMENT
Goal of computation (function
f
)
x
f(x
)
“
user returns
f(x)
?”
“user”
“server”
This talk: f
will be PSPACE-complete
5Slide6
ENVIRONMENT
S
-universal user (for computing
f
)
x
f(x
)
“
user returns
f(x)
?”
S
6Slide7
Formally,U is a
S
-universal user for computing f ifservers S
S
$
poly.
r
unning time for U inputs x, initial states of U & S Pr[ ] ≥ ⅔
S
-universal user (for computing
f
)
On input x with S, U runs poly(|x|)
steps and
U’s final output is f(x)
[JS’08]: can construct universal users for computing PSPACE-complete
f for maximally large class S
7Slide8
110
0110
11110
Problem:
Password-protected servers
ENVIRONMENT
11110
x
f(x
)
8Slide9
Theorem
[JS08,GJS09]
. S-Universal users for classes S containing password-protected servers and goals that require the server to act must run for Ω(2
l
) rounds with servers with passwords of length
l
.
PROMISES MORE THAN WE WANTED!
CAN WE REFINE AWAY PASSWORDS??
9Slide10
Motivation
Beliefs model
Sketch of result
10Slide11
Server’s Beliefs
Q
x
f(x
)
t
U,S
(|x|)
Def’n
:
Q
-Benchmark running time
T
Q
,S
(n) =
E
U
Q
[
tU,S(n)]
I’VE CHOSEN AN
S
WITH POLYNOMIAL Q-BENCHMARK RUNNING TIME
SO,
NO PASSWORD!!
11Slide12
Q
WHY
DOESN’T IT WORK??
PREFIXING A MESSAGE WITH
%!PS-
Adobe
IS THE
MOST
NATURAL THING IN THE
WORLD
.
x
MORAL:
NEED “SIMILAR” BELIEFS…
THAT
ISN’T A
“
PASSWORD.”
12Slide13
Compatibility
P
Q
a
(
P
,
Q
) =
S
w
min
{P(
w
),Q(
w
)} = 1-|P-Q|
TV
13Slide14
Compatibility controls overhead of universal communication
Theorem.
Let P
be a
sampleable
distribution, suppose every server S
S has a belief distribution QS. For PSPACE-complete P, there exist polys r & w such that if strategies from
Q
S
decide
P
with S,
there is a user strategy U
P that computes P
with any SS on x of length n in time
w(1/
a(P, Q )
,n) × (TQ,S o r)(n)
RECALL: “benchmark time” T
Q,S(n) = EU
Q[tU,S
(n)], “compatibility” a(
P, Q ) =
Sw min{P(
w),Q(w)}
Can recover [JS’08] by taking
P
= length-weighted uniform
Q
S
=
δ
U
(S)
(for U(S) helped by S)
DEPENDENCE ON SERVER?
DEPENDENCE ON BENCHMARK TIME W.R.T SERVER BELIEFS
DEPENDENCE ON COMPATIBILE BELIEFS
14Slide15
Key points
Server designers can evaluate benchmark time
w.r.t. their beliefs
Compatible beliefs lead to low overhead (beyond benchmark time)
Beliefs capture natural approaches
15Slide16
Motivation
Beliefs model
Sketch of result
16Slide17
Starting point: [JS’08]
Enumerate algorithms U’:
give each constant share of running time, repeatedly double running time (cf. Levin’73)
Use U’ with S to simulate interactive proof system for
P
, return answer if successful
(exploits efficient
prover strategy using P)
SAMPLE
FROM
P
REPEATEDLY DOUBLE # OF SAMPLES PER TIME BOUND,
INTRODUCE DOUBLED MAXIMUM
TIME
BOUND
High weight in
P
corresponds to short programs in enumeration
17Slide18
Analysis in three easy steps
Markov’s inequality: For poly. r from proof system, U’
Q
S
, see success
w.p
. 1-γif we use U’ run for (1/γ)(TQ,S o
r)(n
) steps
See success
w.p
. 1-γ-
|P-Q|
TV = a(P,
QS
)-γ for U’
P insteadSo, if we run 2/a(
P, QS ) samples from P
for (2/
a(P,
Q ) )(T
Q,S o r)(n) steps each, see success with constant probability
So, try using
γ =
a(P,
QS )/2
w also contains:
overhead from simulating proof system, logarithmic
overhead
in 1/
a
(
P
,
Q
S
)
(
i
distinct bounds in phase
i
)
18Slide19
Compatibility controls overhead of universal communication
Theorem.
Let P
be a
sampleable
distribution, suppose every server S
S has a belief distribution QS. For PSPACE-complete P, there exist polys r & w such that if strategies from
Q
S
decide
P
with S,
there is a user strategy U
P that computes P
with any SS on x of length n in time
w(1/
a(P, Q )
,n) × (TQ,S o r)(n)
RECALL: “benchmark time” T
Q,S(n) = EU
Q[tU,S
(n)], “compatibility” a(
P, Q ) =
Sw min{P(
w),Q(w)}
Actual dependence:Õ
(
1
/
a
(
P
,
Q
)
2
)
19Slide20
RECAP:
We refined the
semantic communication model to capture natural settings in which flexible communication is possible
with low overhead
.
20Slide21
Open problem
Construct
a server with low benchmark running time for a natural goal and belief distribution!
21Slide22
Key points
Server designers can evaluate benchmark time
w.r.t. their beliefs
Compatible beliefs lead to low overhead (beyond benchmark time)
Beliefs capture natural approaches
RECALL:
“benchmark time”
T
Q
,S
(n) =
E
U
Q[tU,S(n)]
RECALL:
“compatibility” a(
P, Q ) = Sw
min{P(w),Q(w)},
overhead is
Õ(1/
a(P
, Q )2
)
FIN.
22